# FY2022 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. Daisuke Takahashi, Postdoctoral Scholar
- Dr. Ardak Kusainova, Postdoctoral Scholar
- Dr. Ayumi Kikkawa, Research Assistant (part time)
- Dr. Chika Hasegawa, Resarch Assistant (part time)
- Ms. Miwako Tokuda, Research Unit Administrator

## 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 intersection numbers for p-spincurves of the moduli spaceMg,n are considered for Dl type by a matrix model. The asymptotic behavior of the large genus g limit and large p limit are derived. The remarkable features of the cases of p = 1/2, −2, −3 are examined in the Laurent expansion for multiple correlation functions. The strong coupling expansions for the negative p cases are considered.

### (b) Knot theory

The knots are derived from a random matrix theory in the replica limit N to 0. The Gaussian means of the product of matrices in the replica limit generate Seifert surface, in which edges describe knot trajectories. The replica formula, which has been used for the evaluation of the intersection numbers, turns out to be useful for generating Seifert surface and associated knot diagrams. The classical knot, which is embedded to three dimensional sphere, is extended to the surface knot by considering time dependent random matrix model.

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

Although the Standard Model (SM) is currently the best theory for explaining the phenomena of elementary particle physics, there are various unsolved problems, and it is necessary to propose and verify New Physics beyond the SM. We proposed and investigated supersymmetric (SUSY) version of the gauged U(1)x extension of the SM, which is one of the attempts of New Physics search. In our model, three right-handed neutrino (RHN) chiral superfields are introduced, R-parity is conserved as usual in the minimal supersymmetric SM (MSSM) even after radiatively breaking the U(1)x symmetry, and the lightest eigenstate of the mixture of the U(1)x gaugino and the fermionic component of one of the RHN chiral superfields appears as another new dark matter (DM) candidate besides the MSSM's lightest neutralino. We have studied cosmological aspects of this DM, analyzed the Large Hadron Collider (LHC) bounds from Z' boson search, and discussed constrains from Big Bang Nucleosynthesis (BBN) for our model.

### 3.3 Random matrix analysis of the chromosome configuration

Using Hi-C data published in the ENCODE project (http://www.encodeproject.org/), we have generated contact matrices for various cancer or normal cells. We investigate the eigenvalue statistics obtained from the Hi-C contact matrices using the method of random matrix theory. By studying the 3-dimensional gene configurations associated with gene-interactions both within and between chromosomes, the specific features of long-range gene interactions in cancer cells can be revealed.

## 4. Publications

### 4.1 Journals

- S. Hikami, Puncture and p spin curves from matrix model III: D type and logarithmic potential. J. Stat. Phys. 188 (2022) 20. https://doi.org/10.1007/s10955-022-02950-2
- Wenliang Li, Ising model close to d=2, Phys. Rev. D105, L091902 (2022)

### 4.2 Books and other one-time publications

S. Hikami, Knots from a random matrix theory with replicas, Michael Fisher memorial book, Edited by A. Ahanony, O. Entin-Wohlman, D. Huse and L. Radzihovsky, to be published WorldScientific (2023).

### 4.3 Oral and Poster Presentations

- Conference / Seminar presentation:
- S. Hikami, Amida-kuji and singularities, in Mini workshop “Various aspect of singularities”, Univ. of Tokyo, March 30-31, 2023.
- S. Hikami, Towards knot theory from random matrices, Silver workshop V. OIST, Nov. 9-11 (2022).
- S. Hikami, Knot, matrix and tensor models …melon or meron?, Quantum gravity, random geometry and holography in Inst. of Henri Poincare. Feb. 9th, 2023.
- Satsuki Oda, Nobuchika Okada, Nathan Papapietro, and Dai-suke Takahashi, “Minimal SUSY U(1)x model with an R-parity conservation,” Progress in Particle Physics 2022 (PPP2022), Yukawa Institute for Theoretical Physics Kyoto University, 2022.08.29
- Dai-suke Takahashi, “Cosmological observations and high energy physics Ⅰ,” Physics Topics II, University of the Ryukyus, 2022.11.29
- Dai-suke Takahashi, “Cosmological observations and high energy physics Ⅱ,” Physics Seminar, University of the Ryukyus, 2023.02.02
- Satsuki Oda, Nobuchika Okada, Nathan Papapietro, and Dai-suke Takahashi, “Minimal SUSY U(1)x model with an R-parity conservation,” 素粒子現象論研究会2022 (High Energy Physics Phenomenology Workshop 2022), Osaka Metropolitan University, Japan, 2023.03.17
- Satsuki Oda, Nobuchika Okada, Nathan Papapietro, and Dai-suke Takahashi, “Minimal SUSY U(1)x model with an R-parity conservation,” JPS 2023 Spring Meeting, Online, Japan, 2023.03.23

## 5. Intellectual Property Rights and Other Specific Achievements

Nothing to report

## 6. Meetings and Events

### 6.1 Mini workshop of singularities

- Date: March 30 and 31, 2023
- Venue: The University of Tokyo, Math. Department, Room 002
- Organizers: Toru Ohmoto, Hiraku Kawanoue, Kei-ichi Watanabe, Shihoko Ishii
- Sponsorship: Kaken-hi and OIST(Mathematical and Theoretical Physics Unit).
- Titles and Abstracts: PDF

### 6.2 Silver workshop (V): Complex geometry and related topics,

- Organizers: Noriko Yui, Kyoji Saito, Shinobu Hikami
- Date: 9 -11th, November 2022
- Venue: OIST-L4E01
- Participants:
Noriko Yui (Queen’s University), Kyoji Saito (TSVP-OIST, RIMS), George Elliott(Toronto Univ.), Shihoko Ishii (The Univ. of Tokyo), Motoko Kato (Ryukyu Univ.), Shinichi Tajima (Niigata Univ.), Makiko Mase (Tokyo Metropolitan Univ.), Mutsuo Oka ( Tokyo Science Univ.), Yoshihisa Saito (Rikkyo Univ.), Andreani Petrou(OIST), Xiaobing Sheng (Univ.of Tokyo), Christine Vespa(Aix-Marseille Univ.), Liron Speyer (OIST), Martin Forsberg Conde(OIST),Todor Milanov (IPMU), Takahiro Saito (RIMS), Shinobu Hikami (OIST)

### 6.3 Seminar: “Superconductivity, magnetism and nematicity in thin films of Fe chalcogenides”

- Date: Monday, June 13, 2022
- Time: 17:00-18:00
- Zoom
- Speaker: A. Maeda, and F. Nabeshima (University of Tokyo)

### 6.4 Seminar: “Drone observation reveals a multilevel society of feral horses”

- Date: Tuesday, March 7, 2023
- Time: 13:30-14:30
- Venue: Lab4 F01 / Zoom
- Speaker: Tamao Maeda (Wildlife Research Center, Kyoto University)

### 6.5 Lecture: “Cosmology I”

- Date: Dec 08, 2022 – Jan 26, 2023 (6 lectures)
- Venue: University of the Ryukyu
- Lecturer: Dai-suke Takahashi (OIST)

## 7. Other

Nothing to report.