Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)  

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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)  

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

Language：English   Publishing type：Research paper (scientific journal)  

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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)  

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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1088/1126-6708/1999/03/012

Publishing type：Doctoral thesis  

Language：English   Publishing type：Research paper (scientific journal)   Publisher：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

Language：English   Publishing type：Research paper (scientific journal)  

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

Publishing type：Master’s thesis  

Language：Japanese   Publisher：The Physical Society of Japan (JPS)