2024/05/10 更新

写真a

クロキ ツネヒデ
黒木 経秀
Tsunehide Kuroki
所属
大学院工学研究科 物質工学分野 理論物理学研究室 教授   
学位
博士(理学) ( 東京大学 )
外部リンク
連絡先
メールアドレス

研究分野

  • 自然科学一般 / 素粒子、原子核、宇宙線、宇宙物理にする理論

主な研究論文

  • Mean field approximation of IIB matrix model and emergence of four-dimensional space-time

    647   153 - 189   2002年12月23日

    Improved perturbation theory and four-dimensional space-time in IIB matrix model

    109 ( 1 )   115 - 132   2003年1月

    Dijkgraaf-Vafa theory as large-N reduction

    Nucl. Phys. B   664   185 - 212   2003年8月4日

    Loops versus matrices: The nonperturbative aspects of noncritical string

    112 ( 1 )   131 - 181   2004年6月

    SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

    876   758 - 793   2013年11月21日

学歴

  • 東京大学   理学系研究科

    - 1998年

      詳細

    国名: 日本国

研究テーマ

  • Resurgenceを用いたwormholeのダイナミクス

    黒木 経秀

    2022年度 - 現在

     詳細

    弦理論と実験の乖離が素粒子物理学における最も深刻な問題の一つであるという認識から、量子重力理論から自然界のパラメーターが決定される初の例を具体的に構成しうるか、という学術的問いの解決に向けて本研究を行う。近年の量子重力理論におけるwormholeの重要性の認識を動機として、具体的には行列模型の連続極限から、wormholeの寄与を予め取り入れた新しい2次元量子重力理論を非摂動的に定義し、その自由エネルギーの満たす微分方程式を導出する。この導出には私が習熟している直交多項式やresurgenceのアイディアを用いる。そしてこの微分方程式から、この理論の宇宙定数がwormholeの足し上げによって決定されるというColemanの機構が成立しているかを検証し、低次元ではあるが量子重力理論の最重要課題を解決している初の例になっていることを具体例により示す。さらに微分方程式からブラックホールの情報喪失問題における量子重力の効果について知見を得る。

    成果:

    2023年度
    Double trace項を含む行列模型の解析法として、character展開が適しているという知見が得られたため、その方向性を検討した。その際得られたアイディアとして、逆に指標展開が可能な行列模型に対してwormholeの寄与を評価する新しい方向性に気づいたため、その検討も行った。具体的には、特に超対称ゲージ理論に付随する行列模型のうちこのクラスに属するものがあり、これらは確かにdouble trace項の和で表されることに注目した。この模型におけるwormholeの寄与について解析することを予定している。また、double trace項を含む行列模型の解析は難しいが、それを含まない行列模型でも同じ連続極限を与える可能性が指摘されていることに気づき、急遽その正当性の解析を行っている。String equation等の提案もなされているため、昨年度我々が求めた摂動級数や非摂動効果が再現されるかを確認することにより、直ちにその正当性が確認可能な状況である。

    2022年度
    本研究の最重要課題の一つはdouble-trace項を含む行列模型の自由エネルギーが満たす微分方程式の導出であるから、まずpotentialおよびdouble-trace項を様々な形に仮定した場合の臨界点を求め、sphere free energy, disk amplitudeやdouble scaling limitの取り方などを同定した。また、sphere topologyにおける臨界指数(string susceptibility)を求めた。この際、従来Das, Dhar, Sengupta and Wadiaによる方法と、Hashimoto and Klebanovによる方法が知られてい
    たが、両者が一致した結果を与えることを具体的な模型で確認した。後者の方が取り扱いが便利なため、両者の等価性を一般的なdouble-trace matrix modelで示す重要性を認識した。さらにこれらの模型において、instanton actionを求めたところ、ポテンシャルやdouble trace項の詳細に依らずにdouble traceがない場合の結果と一致することを確認した。この結果は、double trace項がない行列模型が定義するLiouville理論と、wrong branchを取った場合のLiouville理論が同じ形の非摂動効果を持つことを意味する。あるいは2次元重力の通常のphaseとwormhole-dominant phaseで同じ非摂動効果を持つことを意味している。この結果はdouble-trace matrix modelのfree energyのresurgence構造に重要な示唆を与えるものであり、よって目標とするstring equationの同定に重要な進歩である。

  • BECにおけるHawking輻射

    黒木 経秀

    2023年度 - 現在

     詳細

    BEC Hamiltonianを量子論的に解析することにより、ブラックホールの情報喪失問題解決への知見を得る。BEC Hamiltonianは量子論的にwell-definedであり、またanalog gravityの模型としてblack holeと同様にHawking輻射を起こすことが知られている。よってBEC Hamiltonianの量子論的解析から、微視的にHawking radiation、特にそのentanglement entropyを導出し、Page curve等information lossおいて重要な量を解析し、情報喪失問題解決へ示唆を得ることが本研究の目的である。特に重力理論では取り入れることが困難なback reactionをきちんと取り入れて解析を行う。

    成果:

    2023年度
    まず理論を完全に定義するため、先行研究で考察されている設定がBECとして実際に実現できるか、理論のパラメーターを選ぶことにより調べた。その結果、理論の無矛盾性から、先行研究では見過ごされているいくつかの重要な制限が付くことを発見した。またGross-Pitaevskii方程式において、backgroundとその周りの揺らぎを分離し、逐次両者の高次項を取り入れていくことにより、back reactionが系統的に取り扱えることを示した。この結果に基づき、Hawking radiationによるback reactionを2点関数の形で具体的に求め、それを用いてback reactionを受けた背景中での揺らぎの波動関数を陽な形で求めることに成功した。

論文

  • Replica wormholes from Liouville theory 査読

    Shinji Hirano*, Tsunehide Kuroki

    Journal of High Energy Physics   01 ( 094 )   2022年1月

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer  

    DOI: 10.1007/JHEP01(2022)094

  • Momentum-space entanglement in scalar field theory on fuzzy spheres 査読

    Shoichi Kawamoto*, Tsunehide Kuroki

    Journal of High Energy Physics   12 ( 101 )   2021年12月

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer  

    DOI: 10.1007/JHEP12(2021)101

  • Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings 査読

    Tsunehide Kuroki

    Journal of High Energy Physics   ( 07 )   118   2020年7月

     詳細

    担当区分:筆頭著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer  

    DOI: 10.1007/JHEP07(2020)118

  • Resurgence of one-point functions in a matrix model for 2D type IIA superstrings 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    Journal of High Energy Physics   05 ( 138 )   2019年5月

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer  

  • One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    NUCLEAR PHYSICS B   919   325 - 358   2017年6月 (   ISSN:0550-3213   eISSN:1873-1562 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type HA superstring theory on a Ramond-Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators. 2017 The Author(s). Published by Elsevier B.V.

    DOI: 10.1016/j.nuclphysb.2017.03.018

  • Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models 査読

    Shoichi Kawamoto*, Tsunehide Kuroki

    JOURNAL OF HIGH ENERGY PHYSICS   6 ( 062 )   2015年6月 (   ISSN:1029-8479 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    In the previous study [1-3], we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.

    DOI: 10.1007/JHEP06(2015)062

  • Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    JOURNAL OF HIGH ENERGY PHYSICS   3 ( 006 )   2014年3月 (   ISSN:1029-8479 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In this paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-Ramond background as insertions of the corresponding vertex operators, various IIA amplitudes are explicitly computed including quantitatively precise numerical factors. We show that several kinds of amplitudes in both sides indeed have exactly the same dependence on parameters of the theory. Moreover, we have a number of relations among coefficients which connect quantities in the type IIA theory and those in the matrix model. Consistency of the relations convinces us of the validity of the correspondence.

    DOI: 10.1007/JHEP03(2014)006

  • SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings 査読

    Michael G. Endres*, Tsunehide Kuroki, Fumihiko Sugino*, Hiroshi Suzuki*

    Nuclear Physics. B   876 ( 3 )   758 - 793   2013年11月 (   ISSN:0550-3213 )

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier BV  

    We explicitly compute nonperturbative effects in a supersymmetric double-well
    matrix model corresponding to two-dimensional type IIA superstring theory on a
    nontrivial Ramond-Ramond background. We analytically determine the full
    one-instanton contribution to the free energy and one-point function, including
    all perturbative fluctuations around the one-instanton background. The leading
    order two-instanton contribution is determined as well. We see that
    supersymmetry is spontaneously broken by instantons, and that the breaking
    persists after taking a double scaling limit which realizes the type IIA theory
    from the matrix model. The result implies that spontaneous supersymmetry
    breaking occurs by nonperturbative dynamics in the target space of the IIA
    theory. Furthermore, we numerically determine the full nonperturbative effects
    by recursive evaluation of orthogonal polynomials. The free energy of the
    matrix model appears well-defined and finite even in the strongly coupled limit
    of the corresponding type IIA theory. The result might suggest a weakly coupled
    theory appearing as an S-dual to the two-dimensional type IIA superstring
    theory.

    DOI: 10.1016/j.nuclphysb.2013.09.005

  • New critical behavior in a supersymmetric double-well matrix model 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    Nuclear Physics B   867 ( 2 )   448 - 482   2013年2月 (   ISSN:0550-3213 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier BV  

    We compute various correlation functions at the planar level in a simple supersymmetric matrix model, whose scalar potential is in shape of a double-well. The model has infinitely degenerate vacua parametrized by filling fractions ν ± representing the numbers of matrix eigenvalues around the two minima of the double-well. The computation is done for general filling fractions corresponding to general two-cut solutions for the eigenvalue distribution. The model is mapped to the O(n) model on a random surface with n=-2, and some sector of the model is described by two-dimensional quantum gravity with c=-2 matter or (2, 1) minimal string theory. For the other sector in which such description is not possible, we find new critical behavior of powers of logarithm for correlation functions. We regard the matrix model as a supersymmetric analog of the Penner model, and discuss correspondence of the matrix model to two-dimensional type IIA superstring theory from the viewpoint of symmetry and spectrum. In particular, single-trace operators in the matrix model are naturally interpreted as vertex operators in the type IIA theory. Also, the result of the correlation functions implies that the corresponding type IIA theory has a nontrivial Ramond-Ramond background. © 2012 Elsevier B.V.

    DOI: 10.1016/j.nuclphysb.2012.09.020

  • Renormalization group approach to matrix models via noncommutative space 査読

    Shoichi Kawamoto*, Tsunehide Kuroki, Dan Tomino*

    JOURNAL OF HIGH ENERGY PHYSICS   2012 ( 8 )   2012年8月 (   ISSN:1029-8479 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N - 1) x (N - 1) is obtained by integrating out one row and column of an N x N matrix model, can be regarded as a renormalization group and that its fixed point reveals critical behavior in the large-N limit. We instead utilize the fuzzy sphere structure based on which we construct a new map (renormalization group) from N x N matrix model to that of rank N - 1. Our renormalization group has great advantage of being a nice analog of the standard renormalization group in field theory. It is naturally endowed with the concept of high/low energy, and consequently it is in a sense local and admits derivative expansions in the space of matrices. In construction we also find that our renormalization in general generates multi-trace operators, and that nonplanar diagrams yield a nonlocal operation on a matrix, whose action is to transport the matrix to the antipode on the sphere. Furthermore the noncommutativity of the fuzzy sphere is renormalized in our formalism. We then analyze our renormalization group equation, and Gaussian and nontrivial fixed points are found. We further clarify how to read off scaling dimensions from our renormalization group equation. Finally the critical exponent of the model of two-dimensional gravity based on our formalism is examined.

    DOI: 10.1007/JHEP08(2012)168

  • Deformation of half-BPS solution in ABJM model and instability of supermembrane 査読

    Tsunehide Kuroki, Akitsugu Miwa*, Satoshi Okuda*

    JOURNAL OF HIGH ENERGY PHYSICS   ( 5 )   2011年5月 (   ISSN:1126-6708 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    It is well-known that a supermembrane in the light-cone gauge has a continuous spectrum and is unstable. Physical interpretation of this instability is that a supermembrane can have a long thin tube without cost of energy and consequently it becomes a spiky configuration in which multiple membranes are connected by thin tubes.
    On the other hand, the ABJM model was proposed as a low-energy description of multiple M2-branes in the static gauge. It is natural that an M2-brane is also unstable in this gauge if we believe the physical picture in the light-cone gauge. In order to examine this, we construct a BPS solution explicitly both in the Nambu-Goto action of a supermembrane in the static gauge and in the U(1) x U(1) ABJM model, which represents intersecting M2-branes. Since this configuration is regarded as a single M2-brane emitting another one, we study the instability of an M2-brane by analyzing fluctuations around it. We show that a zero mode exists which can deform the configuration. For comparison, we also examine a similar configuration on the D2-brane and check that it does not have such zero modes under a fixed string charge. Furthermore we confirm that the novel Higgs mechanism translates our BPS solution in the ABJM model into that in the D2-brane world volume theory, where the winding number of the former around the fixed point of the orbifold becomes the number of strings ending on the D2-brane in the latter.

    DOI: 10.1007/JHEP05(2011)011

  • Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    NUCLEAR PHYSICS B   844 ( 3 )   409 - 449   2011年3月 (   ISSN:0550-3213 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work. (C) 2010 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.nuclphysb.2010.11.015

  • Spontaneous supersymmetry breaking in large-N matrix models with slowly varying potential 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    NUCLEAR PHYSICS B   830 ( 3 )   434 - 473   2010年5月 (   ISSN:0550-3213 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size N infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly varying, and the large-N limit is taken with the slowly varying limit.
    First, we explain our formalism, introducing an external field to detect spontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking. It is observed that SUSY is possibly broken even in systems in less than one-dimension, for example, discretized quantum mechanics with a finite number of discretized time steps. Then, we consider spontaneous SUSY breaking in the SUSY matrix models with slowly varying potential, where the external field is turned off after the large-N and slowly varying limit, analogously to the thermodynamic limit in statistical systems. On the other hand, without taking the slowly varying limit, in the SUSY matrix model with a double-well potential whose SUSY is broken due to instantons for finite N, a number of supersymmetric behavior is explicitly seen at large N. It convinces us that the instanton effect disappears and the SUSY gets restored in the large-N limit. (C) 2009 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.nuclphysb.2009.12.021

  • Boundary condition for a D-brane from the Wilson loop, and gravitational interpretation of an eigenvalue in the matrix model in AdS/CFT correspondence 査読

    Shoichi Kawamoto*, Tsunehide Kuroki, Akitsugu Miwa*

    PHYSICAL REVIEW D   79 ( 12 )   1 - 126010   2009年6月 (   ISSN:1550-7998 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:AMER PHYSICAL SOC  

    We study the supersymmetric Wilson loops in the four-dimensional N = 4 super Yang-Mills theory in the context of AdS/CFT correspondence. In the gauge theory side, it is known that the expectation value of the Wilson loops of circular shape with winding number k, W(k) (C), is calculable by using a Gaussian matrix model. In the gravity side, the expectation value of the loop is conjectured to be given by the classical value of the action S(D3) for a probe D3-brane with k electric fluxes as < W(k)(C)> = e(-SD3). Given such correspondence, we pursue the interpretation of the matrix model eigenvalue density, or more precisely the resolvent, from the viewpoint of the probe D3-brane. We see that the position of an eigenvalue appears as the gauge field plus the scalar field integrated over the boundary of the probe D3-brane. In the course of our analysis, we also clarify the boundary condition on the D3-brane in terms of the Wilson loop.

    DOI: 10.1103/PhysRevD.79.126010

  • Production cross section of rotating string 査読

    Tsunehide Kuroki, Toshihiro Matsuo*

    Nuclear Physics B   798 ( 1-2 )   291 - 309   2008年7月 (   ISSN:0550-3213 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We calculate production cross sections of a single rotating string from a collision of two light states in bosonic string theory. We find that the cross sections are written in terms of the modified Bessel function of the first kind with the degree given by the angular momentum in the high energy regime. We also obtain a similar formula from the partial wave expansion of four point amplitudes. Asymptotic behavior of the cross sections is consistent with a well-known form factor of a string. © 2008 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.nuclphysb.2008.02.003

  • Spontaneous supersymmetry breaking by large-N matrices 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    NUCLEAR PHYSICS B   796 ( 3 )   471 - 499   2008年6月 (   ISSN:0550-3213 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking. In particular, in the case of the O'Raifeartaigh model coupled to a certain supersymmetric matrix model, a nonsupersymmetric metastable vacuum appears near the origin of the field space, which is far from the position of the supersymmetric vacuum. We estimate its lifetime as a function of N. (c) 2007 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.nuclphysb.2007.12.003

  • T duality of the Zamolodchikov-Zamolodchikov brane 査読

    Tsunehide Kuroki, Fumihiko Sugino*

    PHYSICAL REVIEW D   75 ( 4 )   044008   2007年2月 (   ISSN:1550-7998 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:AMERICAN PHYSICAL SOC  

    We examine how nonperturbative effects in string theory are transformed under the T-duality in its nonperturbative framework by analyzing the c=1/2 noncritical string theory as a simplest example. We show that in the T-dual theory they also take the form of exp(-S-0/g(s)) in the leading order and that the instanton actions S-0 of the dual Zamolodchikov-Zamolodchikov (ZZ)-branes are exactly the same as those in the original c=1/2 string theory. Furthermore we present formulas for coefficients of exp(-S-0/g(s)) in the dual theory.

    DOI: 10.1103/PhysRevD.75.044008

  • Dynamical generation of non-Abelian gauge group via the improved perturbation theory 査読

    T. Aoyama*, T. Kuroki, Y. Shibusa*

    PHYSICAL REVIEW D   74 ( 10 )   2006年11月 (   ISSN:1550-7998 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:AMERICAN PHYSICAL SOC  

    It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It also gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua.

    DOI: 10.1103/PhysRevD.74.106004

  • Universality of nonperturbative effects in c<1 noncritical string theory 査読

    Nobuyuki Ishibashi*, Tsunehide Kuroki, Atsushi Yamaguchi*

    Journal of High Energy Physics   ( 9 )   1123 - 1138   2005年9月 (   ISSN:1029-8479 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Nonperturbative effects in c &lt
    1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been calculated so far. Using the method proposed recently, we show that it is possible to determine the coefficients for (p,q) string theory. We find that they are indeed finite in the double scaling limit and universal in the sense that they do not depend on the details of the potential of the two-matrix model. © SISSA 2005.

    DOI: 10.1088/1126-6708/2005/09/043

  • Universality of nonperturbative effect in type 0 string theory 査読

    Hikaru Kawai*, Tsunehide Kuroki, Yoshinori Matsuo*

    Nuclear Physics B   711 ( 1-2 )   253 - 274   2005年4月 (   ISSN:0550-3213 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We derive the nonperturbative effect in type 0B string theory, which is defined by taking the double scaling limit of a one-matrix model with a two-cut eigenvalue distribution. However, the string equation thus derived cannot determine the nonperturbative effect completely, at least without specifying unknown boundary conditions. The nonperturbative contribution to the free energy comes from instantons in such models. We determine by direct computation in the matrix model an overall factor of the instanton contribution, which cannot be determined by the string equation itself. We prove that it is universal in the sense that it is independent of the detailed structure of potentials in the matrix model. It turns out to be a purely imaginary number and therefore can be interpreted as a quantity related to instability of the D-brane in type 0 string theory. We also comment on a relation between our result and boundary conditions for the string equation. © 2005 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.nuclphysb.2005.01.002

  • Direct derivation of the Veneziano-Yankielowicz superpotential from matrix model 査読

    Hikaru Kawai*, Tsunehide Kuroki, Takeshi Morita*, Kensuke Yoshida*

    PHYSICS LETTERS B   611 ( 3-4 )   269 - 278   2005年4月 (   ISSN:0370-2693   eISSN:1873-2445 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    We derive the Veneziano-Yankielowicz superpotential directly from the matrix model by fixing the measure precisely. The essential requirement here is that the effective superpotential of the matrix model corresponding to the N = 4 supersymmetric Yang-Mills theory vanishes except for the tree gauge kinetic term. Thus we clarify the reason why the matrix model reproduces the Veneziano-Yankielowicz superpotential correctly in the Dijkgraaf-Vafa theory. (c) 2005 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.physletb.2005.02.032

  • Loops versus matrices - The nonperturbative aspects of noncritical string 査読

    Masanori Hanada*, Masashi Hayakawa*, Nobuyuki Ishibashi*, Hikaru Kawai*, Tsunehide Kuroki, Yoshinori Matsuo*, Tsukasa Tada*

    PROGRESS OF THEORETICAL PHYSICS   112 ( 1 )   131 - 181   2004年7月 (   ISSN:0033-068X )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

    The nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This implies that it may not be possible to formulate string theory nonperturbatively solely in terms of closed strings.

    DOI: 10.1143/PTP.112.131

  • Supersymmetric large-N reduced model with multiple matter 査読

    Hikaru Kawai*, Tsunehide Kuroki, Takeshi Morita*

    Nucl.Phys. B683 (2004) 27-47   B683 ( 1/2 )   27 - 47   2003年12月 (   ISSN:0550-3213 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We showed in hep-th/0303210 that the Dijkgraaf-Vafa theory can be regarded as<br />
    large-N reduction in the case of $\mathcal{N}=1$ supersymmetric U(N) gauge<br />
    theories, with single adjoint matter. We generalize this to gauge theories with<br />
    gauge groups being the products of some unitary groups coupled to bifundamental<br />
    or fundamental matter. We show that some large-N reduced models of these<br />
    theories are supermatrix models, whose free energy is equivalent to the<br />
    prepotentials of the original gauge theories. The supermatrix model in our<br />
    approach should be taken in the Veneziano limit $N_c,N_f \to \infty $ with<br />
    $N_f/N_c$ fixed.

    DOI: 10.1016/j.nuclphysb.2004.02.005

  • Dijkgraaf-Vafa theory as large-N reduction 査読

    Hikaru Kawai*, Tsunehide Kuroki, Takeshi Morita*

    NUCLEAR PHYSICS B   664 ( 1-2 )   185 - 212   2003年8月 (   ISSN:0550-3213   eISSN:1873-1562 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    We construct a large-N twisted reduced model of the four-dimensional super-Yang-Mills theory coupled to one adjoint matter. We first consider a non-commutative version of the four-dimensional superspace, and then give the mapping rule between matrices and functions on this space explicitly. The supersymmetry is realized as a part of the internal U(infinity) gauge symmetry in this reduced model. Our reduced model can be compared with the Dijkgraaf-Vafa theory that claims the low-energy glueball superpotential of the original gauge theory is governed by a simple one-matrix model. We show that their claim can be regarded as the large-N reduction in the sense that the one-matrix model they proposed can be identified with our reduced model. The map between matrices and functions enables us to make direct identities between the free energies and correlators of the gauge theory and the matrix model. As a by-product, we can give a natural explanation for the unconventional treatment of the one-matrix model in the Dijkgraaf-Vafa theory where eigenvalues lie around the top of the potential. (C) 2003 Elsevier B.V. All rights reserved.

    DOI: 10.1016/S0550-3213(03)00408-5

  • Improved perturbation theory and four-dimensional space-time in the IIB matrix model 査読

    Hikaru Kawai*, Shoichi Kawamoto*, Tsunehide Kuroki, Shun'ichi Shinohara*

    PROGRESS OF THEORETICAL PHYSICS   109 ( 1 )   115 - 132   2003年1月 (   ISSN:0033-068X )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

    We have analyzed the 1113 matrix model on the basis of the improved mean field approximation (IMFA) and have obtained evidence suggesting that the four-dimensional space-time appears as its most stable vacuum. This method is a systematic way to obtain an improved perturbation series and was first applied to the IIB matrix model by Nishimura and Sugino. In a previous paper, we reformulated this method and proposed a criterion for the convergence of the improved series, that is, the appearance of a "plateau". In this paper, we carry out higher-order calculations, and find that our improved free energy tends to have a plateau, which shows that IMFA works well in the 1113 matrix model.

    DOI: 10.1143/PTP.109.115

  • Mean field approximation of IIB matrix model and emergence of four-dimensional space-time 査読

    H Kawai*, S Kawamoto*, T Kuroki, T Matsuo*, S Shinohara*

    NUCLEAR PHYSICS B   647 ( 1-2 )   153 - 189   2002年12月 (   ISSN:0550-3213 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    For the purpose of analyzing non-perturbative dynamics of string theory, Nishimura and Sugino have applied an improved mean field approximation (IMFA) to IIB matrix model, We have extracted the essence of the IMFA and obtained a general scheme, the improved Taylor expansion, that can be applied to a wide class of series which is not necessarily convergent. This approximation scheme with the help of the 2PI free energy enables us to perform higher order calculations. We have shown that the value of the free energy is stable at higher orders, which supports the validity of the approximation. Moreover. the ratio between the extent of "our" space-time and that of the internal space is found to increase rapidly as we take the higher orders into account. Our results suggest that the four-dimensional space-time emerges spontaneously in IIB matrix model. (C) 2002 Elsevier Science B.V. All rights reserved.

    DOI: 10.1016/S0550-3213(02)00908-2

  • Strings as flux tube and deconfinement on branes in gauge theories 査読

    Hikaru Kawai*, Tsunehide Kuroki

    PHYSICS LETTERS B   518 ( 3-4 )   294 - 300   2001年10月 (   ISSN:0370-2693 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    We propose gauge theories in which the unstable branes and the fundamental string are realized as classical solutions. While the former are represented by domain wall like configurations of a scalar field coupled to the gauge field, the latter is by a confined flux tube in the bulk. It is shown that the confined flux tube is really a source of the bulk B-field. Our model also provides a natural scenario of the confinement on the brane in the context of the open string tachyon condensation. It is also argued that the fundamental string can be realized as a classical solution in a certain IIB matrix model as in our model. (C) 2001 Published by Elsevier Science B.V.

    DOI: 10.1016/S0370-2693(01)01079-6

  • Time-delay at higher genus in high-energy open string scattering 査読

    Tsunehide Kuroki, Soo-Jong Rey*

    PHYSICS LETTERS B   499 ( 1-2 )   158 - 166   2001年2月 (   ISSN:0370-2693   eISSN:1873-2445 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    We explore some aspects of causal time-delay in open string scattering studied recently by Seiberg, Susskind and Toumbas. By examining high-energy scattering amplitudes at higher order in perturbation theory, we argue that causal time-delay at Gth order is 1/(G + 1) times smaller than the time-delay at tree level. We propose a space-time interpretation of the result by utilizing the picture of the high-energy open string scattering put forward by Gross and Mafies. We argue that the phenomenon of reduced time-delay is attributed to the universal feature of the space-time string trajectory in high-energy scattering that string shape at higher order remains the same as that at tree level but overall scale is reduced. We also discuss implications to the space-time uncertainty principle and make brief comments on causal time-delay behavior in space/time noncommutative field theory. (C) 2001 Published by Elsevier Science B.V.

    DOI: 10.1016/S0370-2693(01)00034-X

  • Noncommutativities of D-branes and theta-changing degrees of freedom in D-brane matrix models 査読

    Tsunehide Kuroki

    PHYSICS LETTERS B   481 ( 1 )   97 - 106   2000年5月 (   ISSN:0370-2693   eISSN:1873-2445 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER SCIENCE BV  

    It is known that when there are several D-branes, their space-time coordinates in general become noncommutative. From the point of view of noncommutative geometry, it reflects noncommutativity of the world volume of the D-branes. On the other hand, as we showed in the previous work, in the presence of the constant antisymmetric tensor field the momentum operators of the D-branes have noncommutative structure. In the present paper, we investigate a relation between these noncommutativities and the description of D-branes in terms of the noncommutative Yang-Mills theory recently proposed by Seiberg and Witten. It is shown that the noncommutativity of the Yang-Mills theory, which implies that uf the world volume coordinates, originates from both noncommutativities of the transverse coordinates and momenta from the viewpoint of the lower-dimensional D-branes. Moreover, we show that this noncommutativity is transformed by coordinate transformations on the world volume and thereby can he chosen in an arbitrary fixed value. We also make a brief comment on a relation between this fact and a hidden symmetry of the IIB matrix models. (C) 2000 Elsevier Science B.V. All rights reserved.

    DOI: 10.1016/S0370-2693(00)00418-4

  • Master field on a fuzzy sphere 査読

    Tsunehide Kuroki

    Nuclear Physics B   543 ( 1-2 )   466 - 484   1999年3月 (   ISSN:0550-3213 )

     詳細

    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier  

    The O(N)-invariant field theory is considered on both an ordinary and a non-commutative sphere (fuzzy sphere). It is shown that in both cases large-N dominant fields (master fields) exist and their explicit forms an: presented. They are found to mix the internal symmetry and the (fuzzy) space-time symmetry. It is also argued that the cutoff introduced by the fuzzy sphere plays an essential role in constructing the master field. © 1999 Elsevier Science B.V.

    DOI: 10.1016/S0550-3213(98)00815-3

  • World volume noncommutativity versus target space noncommutativity 査読

    Mitsuhiro Kato*,Tsunehide Kuroki

    1999 ( 03 )   1999年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    DOI: 10.1088/1126-6708/1999/03/012

  • Master Fields on Fuzzy Sphere

    Tsunehide Kuroki

    1998年3月

     詳細

    掲載種別:学位論文(博士)  

  • Manifestly T-duality symmetric matrix models 査読

    Tsunehide Kuroki, Yuji Okawa*, Fumihiko Sugino*, Tamiaki Yoneya*

    PHYSICAL REVIEW D   55 ( 10 )   6429 - 6437   1997年5月 (   ISSN:0556-2821 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:AMERICAN PHYSICAL SOC  

    We present a new class of matrix models which are manifestly symmetric under the T-duality transformation of the target space. The models may serve as a nonperturbative regularization for the T-duality symmetry in continuum string theory. In particular, it now becomes possible to extract winding modes explicitly in terms of extended matrix variables.

    DOI: 10.1103/PhysRevD.55.6429

  • T-duality transformation and universal structure of noncritical string field theory 査読

    Takashi Asatani*, Tsunehide Kuroki, Yuji Okawa*, Fumihiko Sugino*, Tamiaki Yoneya*

    Physical Review D - Particles, Fields, Gravitation and Cosmology   55 ( 8 )   5083 - 5111   1997年4月 (   ISSN:1550-2368 )

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We discuss a [Formula presented]-duality transformation for the [Formula presented] matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the [Formula presented] model in the scaling limit is [Formula presented]-duality symmetric in the sphere approximation. In the case of the standard two-matrix model, however, the duality symmetry is violated when the higher-genus effects are taken into account, due to the nonsymmetrical appearence of global [Formula presented] vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by Sugino and Yoneya are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators. © 1997 The American Physical Society.

    DOI: 10.1103/PhysRevD.55.5083

  • 位相的重力におけるヴィラソロ拘束条件

    黒木 経秀

    東京大学   1995年3月

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    掲載種別:学位論文(修士)  

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MISC

  • Renormalization group approach to matrix models via noncommutative space 査読

    Tsunehide Kuroki, Shoichi Kawamoto*, Dan Tomino*

    Fortschritte der Physik   62 ( 9-10 )   792 - 796   2014年5月 (   ISSN:0015-8208 )

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    記述言語:英語   出版者・発行元:Wiley  

    DOI: 10.1002/prop.201400032

  • 27aSA-3 Spontaneous supersymmetry breaking in noncritical covariant superstring theory

    黒木 経秀

    日本物理学会講演概要集   69 ( 1 )   1 - 1   2014年3月 (   ISSN:1342-8349 )

     詳細

    記述言語:日本語   出版者・発行元:一般社団法人日本物理学会  

  • LARGE-N RENORMALIZATION GROUP ON FUZZY SPHERE 査読

    SHOICHI KAWAMOTO*, DAN TOMINO*, TSUNEHIDE KUROKI

    International Journal of Modern Physics: Conference Series   21   151 - 152   2013年1月 (   ISSN:2010-1945   eISSN:2010-1945 )

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    記述言語:英語   出版者・発行元:World Scientific Pub Co Pte Lt  

    We study the large-N renormalization group of scalar field theory on a fuzzy sphere. We carry out perturbative analysis and formulate the renormalization group equation. We then search for fixed points and investigate their properties.

    DOI: 10.1142/s2010194513009562

  • SPONTANEOUS SUPERSYMMETRY BREAKING BY LARGE-N MATRICES

    TSUNEHIDE KUROKI, FUMIHIKO SUGINO*

    International Journal of Modern Physics A   23 ( 14n15 )   2192 - 2194   2008年6月 (   ISSN:0217-751X   eISSN:1793-656X )

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    記述言語:英語   出版者・発行元:World Scientific Pub Co Pte Lt  

    Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity.

    DOI: 10.1142/s0217751x08040809

  • Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory

    Tsunehide Kuroki

    Progress of Theoretical Physics Supplement   171   117 - 120   2007年8月 (   ISSN:0375-9687 )

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    記述言語:英語   出版者・発行元:Oxford University Press (OUP)  

    DOI: 10.1143/ptps.171.117

  • 29a-YQ-3 明白なT-duality対称性を持つ行列模型

    黒木 経秀, 大川 祐司*, 杉野 文彦*, 米谷 民明*

    日本物理学会講演概要集   52 ( 1 )   5 - 5   1997年3月 (   ISSN:1342-8349 )

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    記述言語:日本語   出版者・発行元:一般社団法人日本物理学会  

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書籍等出版物

  • PROCEEDINGS OF THE NINETEENTH WORKSHOP ON GENERAL RELATIVITY AND GRAVITATION IN JAPAN

    黒木 経秀( 担当: 共著)

    JGRG 全427頁  2009年12月 

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    著書種別:学術書

  • Quantum Theory & Symmetries 4

    黒木 経秀( 担当: 共著)

    Heron Press 全1482頁  2006年9月 

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    著書種別:学術書

  • String Theory

    黒木 経秀( 担当: 共著)

    American Institute of Physics 全366頁  2002年1月 

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    著書種別:学術書

講演・口頭発表等

  • Replica wormholes and defects in JT gravity from Liouville theory 国際会議

    Tsunehide Kuroki

    Randomness, Integrability and Representation Theory in Quantum Field Theory 2021  ( Online )   2021年3月  Osaka City University

     詳細

    会議種別:口頭発表(一般)  

    We consider replica wormholes and defects in JT gravity in terms of boundary Liouville theory. We first make precise connection between the JT gravity and semiclassical Liouville theory. In particular, we clarify how nontrivial physics associated with dilaton in the former is encoded into the latter. According to this dictionary, we can reproduce the precise form of contribution from the replica wormhole to the generalized entropy by applying the replica trick directly to the Liouville theory. Here it is remarkable that even the contribution from the boundary dilaton can be also exactly retrieved. Our dictionary also enables us to identify defects in the JT gravity as the deformation of the Liouville action.

受賞

  • 第8回中村誠太郎賞

    2013年9月   素粒子奨学会  

    黒木経秀

科学研究費補助金

  • Resurgenceを用いたwormholeのダイナミクスの解明 研究代表者

    課題番号:22K03606 基盤研究(C) 2022年度 ~ 2025年度

    黒木 経秀

  • Resurgenceによる超弦理論における超対称性の破れの解明 研究代表者

    課題番号:19K03834 基盤研究(C)

    黒木 経秀

担当科目(学内) ※授業フィードバックは学内ネットワークからのみ閲覧可能です。

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教育内容・方法の工夫

  • 演習での工夫

     詳細

    講義で教員の話を聞いてノートを取るだけでは物理学は身に付かず、やはり自分で問題に際し考え計算を行うことが重要である。「力学1および演習」の演習中は教科書、ノート、参考書等参照可、教員やTAによるヒント出しも有とし、学生が実際に問題に当たった時、自分自身何が分かっていないのかを把握してもらうことを最大の目的とした。

  • 書き込み式プリントによる授業

     詳細

    「力学1および演習」、「電磁気学1」、「量子力学1」、「現代物理学特論」において、穴埋め式のプリントを作成し、学生は講義中に重要な式や図、語句のみを書き込むことができるようにした。作成に当たっては自ら書き込んでみて構成、空白、内容の提示の方法を綿密に計算、取捨選択した。これにより、メリハリのある効率的な講義を行うことができた。また、まとめの欄を作りそれに書き込んでもらうことにより、学生の自らのまとめのページが自動的に構成できるようにし、知識の整理、復習、定着に役立つようにした。

作成した教材

  • 書き込み式プリント(2019年度~2021年度)

     詳細

    「力学1および演習」、「電磁気学1」、「量子力学1」、「現代物理学特論」において、穴埋め式のプリントを作成し、学生は講義中に重要な式や図、語句のみを書き込むことができるようにした。作成に当たっては自ら書き込んでみて構成、空白、内容の提示の方法を綿密に計算、取捨選択した。これにより、メリハリのある効率的な講義を行うことができた。また、まとめの欄を作りそれに書き込んでもらうことにより、学生の自らのまとめのページが自動的に構成できるようにし、知識の整理、復習、定着に役立つようにした。