# FY2020 Annual Report

**Mathematical and Theoretical Physics Unit
Shinobu Hikami**

## Abstract

Mathematical and theoretical physics unit studied the subjects related to random matrix theory and conformal field theory. The intersection numbers of the moduli space of p-spin curves and the conformal bootstrap method for higher dimensions were two main subjects, in addition to study of the biological systems.

## 1. Staff

- Prof. Shinobu Hikami, Professor
- Dr. Satsuki Oda, Staff Scientist
- Dr. Wenliang Li, Postdoctoral Scholar
- Dr. Daisuke Takahashi, Postdoctoral Scholar
- Dr. Ayumi Kikkawa, Research Assistant (part time)
- Dr. Chika Hasegawa, Resarch Assistant (part time)
- Ms. Miwako Tokuda, Research Unit Administrator
- Mr. Adrian David, PhD Student (Graduated)

## 2. Collaborations

### 2.1 Collaborations with University of Tokyo

- Description: Moduli space and matrix models:
- The study of higher Teichmuller space and various topological invariances.

- Researcher: Prof. N. Kawazumi (University of Tokyo)

### 2.2 Collaborations with Ecole Normale Superieure

- Description: Random matrix theory with an external source and topological field theory
- Researcher: Prof. Edouard Brezin (lpt, ENS, Paris)

## 3. Activities and Findings

### 3.1 Random matrix theory (S. Hikami)

(a) Matrix models and topological invariants

The matrix model of the moduli space was studied for p-spin curves, and extended to the half integer spin p=1/2+ n. This case is related to the Ramond punctures on the Riemann surfaces and the new method of evaluation is presented (E. Brezin and S. Hikami, Punctures and p-spin curves from matrix models, J. Stat. Phys.). Further, string equation and three-point functions were studied (E. Brezin and S. Hikami, Punctures and p-spin curves from matrix models II, J. Stat. Phys.). The singularity theory of ADE types was studied by matrix models, and the intersection numbers of D type were derived. The relation to open intersection numbers were clarified (in preparation to publish). The spectral form factor of the time dependent matrix model was considered, and the universality of the quantum chaos was discussed near the Heisenberg time (A. Mukherjee and S. Hikami, JHEP).

### (b) Bootstrap analysis for random magnetic field Ising model

By the determinant bootstrap method, the relation of a random field Ising model and a pure Ising model was studied. This relation was suggested by a supersymmetric theory, but this relation does not hold below a critical dimension. This breakdown was obtained by the determinant bootstrap method. We find the dimensional reduction of the d dimensional random magnetic field to pure Ising model does not work under d=4.5 dimensions. (talk in OIST workshop and in preparation to publish).

### 3.2 Analytic conformal bootstrap (Wenliang Li)

For the analytic bootstrap studies of conformal field theories, it is important to have general analytic expressions of conformal blocks near the lightcone. Base on the previous work (JHEP 01 (2020) 055), we found the all-order analytic expression of 4-point scalar conformal blocks (JHEP 06 (2020) 105). In a more recent work (JHEP05(2021)128), we obtained the general formulae in factorized form. This leads to a new understanding of the higher spin case, which now has a very simple structure. The resummation of large spin tails can be carried out straightforwardly and the effects of complete Regge trajectories can be investigated more systematically.

### 3.3 Extended SUSY and non-SUSY models of the Standard Model (S. Oda, D.-s. Takahashi)

Although the Standard Model (SM) is the best theory in describing elementary particle physics phenomena, it suffers from several problems, such as the electroweak vacuum unstability problem, the gauge hierarchy problem, etc. In order to solve these problems, we have investigated several extended models of the SM. We focused on the DFSZ axion model with the classically scale invariance at the Planck scale, which can be reduced to the Two-Higgs Doublet Model (THDM) in the low-energy scale. We discussed the high scale validity of the Higgs sector, namely the absence of Landau poles and the vacuum stability, and found that the high scale validity tightly constrains the parameter region. We also study the supersymmetric version of the gauged U(1)x extension of the SM, where R-parity is conserved as usual in the MSSM, since supersymmetric extension is a promising way to solve the gauge hierarchy problem in the SM. In our model, the lightest eigenstate of the mixture of the U(1)x gaugino and the fermionic component of one of the right-handed neutrino chiral superfields appears as a new dark matter candidate. We have investigated phenomenology of this dark matter particle, and have searched allowed parameter regions to satisfy the cosmological constrains and Large Hadron Collider (LHC) bounds.

### 3.4 The statistical analysis of 3D chromatin conformation (A. Kikkawa)

Using huge amounts of published Hi-C experimental data, we investigate statistical universality in the chromosome folding architecture. The contact matrices show interactions between the chromosome domains, and they reveal hierarchical structures including the TADs (topologically associating domains). The statistical analyses of the contact matrices or Hi-C maps provide valuable insights of the 3-dimensional chromosome structures in the nucleus.

## 4. Publications

### 4.1 Journals

- E. Brezin and S. Hikami, Puncture and p spin curves from matrix models, J. Stat. Phys. (2020) 180:1031-1060. doi.org/10.1007/s10955-020-02581-5
- A. Mukherjee and S. Hikami, Spectral form factor for time-dependent matrix model, JHEP 03(2021) 071. doi.org/10.1007/JHEP03(2021)071.
- S. Hikami and E. Brezin, Puncture and p spin curves from matrix model II. J. Stat. Phys.183 (2021) 36. doi.org/10.1007/s10955-021-02776-4
- Wenliang Li, Lightcone expansions of conformal blocks in closed form, J. High Energ. Phys. 2020, 105 (2020). https://doi.org/10.1007/JHEP06(2020)105
- Wenliang Li, Factorized lightcone expansion of conformal blocks, J. High Energ. Phys. 2021, 128 (2021). https://doi.org/10.1007/JHEP05(2021)128

### 4.2 Books and other one-time publications

Nothing to report

### 4.3 Oral and Poster Presentations

- Conference presentation:
- S. Hikami, Singularities and conformal bootstrap for curves, OIST workshop, Feb. 12, 2021. (zoom conference).
- Wenliang Li, Analytically solving the Ising model in 2+ε dimensions, 2021-May-10, Bootstat 2021: Conformal bootstrap and statistical models, (1.5 hour)
- Wenliang Li, Conformal bootstrap near the lightcone, 2020-June-12, advanced workshop on gravity and cosmology, Dalian University of Technology, China (45 minutes)
- Satsuki Oda, Yutaro Shoji, and Dai-suke Takahashi, High Scale Validity of the DFSZ Axion Model with Precision, Progress in Particle Physics 2020 (PPP2020), Yukawa Institute for Theoretical Physics Kyoto University, 2020.08.31
- Satsuki Oda, Nobuchika Okada, Nathan Papapietro, and Dai-suke Takahashi ,U(1)x extended MSSM with conserving R-parity, JPS 2020 Autumn Meeting, University of Tsukuba, 2020.09.15

- Seminar:
- Wenliang Li, Analytic origin of conformal bootstrap kinks?, 2021-April-16, Yukawa Institute for Theoretical Phyiscs, Kyoto University (1 hour)
- Wenliang Li, Conformal bootstrap near the lightcone, 2020-April-02, Center for joint quantum studies, Tianjin University, China (1 hour)
- Dai-suke Takahashi, Gauged U(1)’ extended Standard Model (with Classically Conformal Invariance), Physics Topics II, University of the Ryukyus, 2020.11.17
- Dai-suke Takahashi, Elementary Particle Physics and Cosmology II, Physics Seminar, University of the Ryukyus, 2021.02.04

## 5. Intellectual Property Rights and Other Specific Achievements

Nothing to report

## 6. Meetings and Events

### 6.1 Quantum math, singularities and applications, OIST 2020 workshop

- Monday, February 8, 2021 to Friday, February 12, 2021
- Venue OIST (Zoom)
- Organizers:
- S. Ishii (Univ. of Tokyo)
- Y. Kawahigashi (University of Tokyo)
- Shinobu Hikami(OIST)

- Invited speakers:
- Shihoko Ishii (The University of Tokyo)
- Lawrence Ein (University of Illinois at Chicago)
- Kei-ichi Watanabe (Nihon University)
- Yasuyuki Kawahigashi (The University of Tokyo)
- Vladimir Dotsenko (Univ. Strasbourg)
- Benoit Collins (Kyoto University)
- Shunsuke Takagi (The University of Tokyo)
- Kohsuke Shibata (Nihon University)
- Takehiko Yasuda (Osaka University)
- Zhenghan Wang (Microsoft Station Q)
- Kyoji Saito (Kyoto Univ. RIMS)
- Shinobu Hikami (OIST)
- Masahiko Yoshinaga (Hokkaido University)
- Terry Gannon(University of Alberta)
- Motoko Kato (Ehime University)
- Makiko Mase (Mannheim University)
- Mayuko Yamashita (Kyoto Univ. RIMS)

### 6.2 Lecture:

- Elementary Particle Physics and Cosmology II (Standard Model and the Beyond)
- Date: Nov 26, 2020 – Jan 28, 2021 (6 lectures)
- Venue: University of the Ryukyus
- Lecturer: Dai-suke Takahashi (OIST)

## 7. Other

Nothing to report.