One of the most serious problems in particle physics is that separation between string theory and experiment. This situation leads us to initiate this study with aim to resolve an academic question whether it is possible to construct the first example in which parameters in nature can be fixed by theory of quantum gravity. Motivated by recent understanding of importance of wormhole effect in theory of quantum gravity, we define concretely and nonperturbatively new theory of two-dimensional quantum gravity including contribution of wormholes in advance by taking a continuum limit of a matrix model. We furthermore derive a differential equation for its free energy. In this derivation, we adopt techniques of orthogonal polynomials, or idea of resurgence with which I am familiar. From the equation we confirm the idea by Coleman that the cosmological constant is determined by sum over wormholes and thus we show that our model is indeed the first example that resolves one of the most important problems in quantum gravity, although it is in lower dimensions. Moreover, from the differential equation we get some insight into effect of quantum gravity in information loss problem of black hole.

Outcome：

2024
We derived the disk amplitude in the matrix model with a double trace term. We got strong evidence of universality by confirming that the disk amplitudes in different choices of the double-trace term agree. Furthermore, since there are two proposals to reach the wormhole-dominant phase, we checked that they give the same result and confirmed their equivalence. The disk amplitude we have obtained takes exactly the same form as in the pure-gravity phase. Since it is a highly nontrivial fact, we gave the reason for it from the Liouville theory point of view. On the other hand, in all previous studies the coupling constant in the double-trace term was fixed on its critical value. Hence we took the continuum limit in such a way that it is away from the critical value and then introduced a renormalized wormhole coupling for the first time. We found that the disk amplitude depends only on a particular combination of the bulk cosmological constant and the wormhole coupling, and that thereby the former can be zero by fine-tuning of the latter.

We get insights into resolution of information loss problem of black hole by analyzing the BEC Hamiltonian in quantum mechanical manner. The BEC Hamiltonian is well-defined quantum mechanically, and it is known to have Hawking radiation as a model of analog gravity. We thus derive Hawking radiation and its entanglement entropy by quantum mechanical analysis of BEC Hamiltonian and investigate various quantities like Page curve which play important role in information loss problem, The aim of this study is to get insights into resolution of information loss problem through these analyses. In particular, we take account of effect of back reaction consistently which is difficult to do in theory of real gravity.

Outcome：

2024
It is necessary to know an explicit form of mode functions both inside and outside the horizon in order to get the Bogoliubov coefficients. Although it has been obtained in the literature, it may not be fully justified due to nontrivial form of the classical configuration of interest in this study. We clarified conditions for justification of known mode functions. Furthermore, we recognized that the connection formula itself is highly nontrivial since the background under consideration changes drastically at the horizon. Hence we elaborated on it through the Bogoliubov equation. Then we have derived the Bogoliubov coefficients before taking account of backreaction.

2023
In order to define our BEC theory, we fix parameters in the BEC Hamiltonian in such a way that it realizes the set up considered in the literature. As a result, we find that there are some important restrictions from consistency of the theory which are overlooked in the literature. We also show that back reaction can be taken into account in systematic manner by separating background and fluctuation around it in the Gross-Pitaevskii equation, and considering them iteratively. Based on this observation, we derive back reaction from Hawking radiation as a two-point function, and by using it, we can obtain explicitly a wave function of fluctuation around background subject to back reaction.