FY2021 Annual Report

Mathematical and Theoretical Physics Unit
Shinobu Hikami

Silver Workshop, January 2021

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

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.  ADE singularities are investigated, and D type singularity is shown to be related to the logarithmic potential. The intersection numbers of genus g for D type is obtained for all genus. In the large g limit, an asymptotic behavior is reduced from a matrix model. (J. Stat. Phys. To be published). The intersection numbers for E6, E7 and E8 singularities are considered, which are related to Seiberg-Witten potential.

Rarita-Schwinger s=3/2 spin is studied in the connection to the recently discovered topological (Half-Heusler) materials of s=3/2 in the p-spin curves of moduli space.

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

The Standard Model (SM) is the most successful theory of particle physics. However, the theoretical developments are needed to explain the deficiencies of the SM, such as the gauge hierarchy problem, non-zero neutrino mass, no candidate of dark matter, etc. To solve these problems, we have investigated several extended models of the SM. We proposed the supersymmetric version of the gauged U(1)x extension of the SM, where R-parity is conserved as usual in the minimal supersymmetric Standard Model (MSSM), since supersymmetric extension is a promising way to solve the gauge hierarchy problem in the SM. Since R-parity is conserved, the lightest neutralino is a prime candidate of the dark matter as usual. 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 various phenomenological aspects of our model.

3.3 The statistical analysis of 3D genome  (A. Kikkawa)

Using Hi-C data published in the ENCODE project (http://www.encodeproject.org/), we have generated contact matrices for various cancer or normal (primary) cells. We investigate the eigenvalues statistics obtained from the Hi-C contact matrices with the method of the random matrix theory.  It is already known that the chromosomal structural variants in cancer cells are important in the study of oncogenesis.  By studying the 3-dimensional gene configurations related to the gene-interactions both within the chromosome and inter-chromosomes, the specific features of the long-range gene interactions in cancer cells can be revealed.   

  With the random matrix theory, we found that the contact matrices exhibit the universal (Wigner-Dyson) eigenvalues spacing distributions: P(s), both intra-chromosomal and inter-chromosomal contact maps. Furthermore, we focused on ratios of number of eigenvalues unfolded (NUE).  We found the NUEs in the inter-chromosomal contact matrices show more sample specific behavior in cancer cells compared to the normal cells.

4. Publications

4.1 Journals

  • 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
  • S. Hikami, Puncture and p spin curves from matrix model III: D type and logarithmic potential. J. Stat. Phys. (Accepted), arXiv: 2111.13793.
  • Wenliang Li, Ising model close to d=2, Phys. Rev. D105, L091902 (2022)
  • Wenliang Li, Factorized lightcone expansion of conformal blocks, JHEP 2021, 128 (2021),　https://doi.org/10.1007/JHEP05(2021)128
  • Wenliang Li, Ising model close to d=2, arXiv:2107.13679

4.2 Books and other one-time publications

Nothing to report

4.3 Oral and Poster Presentations

  • Conference / Seminar presentation:
    • S. Hikami, Modularity and links in the intersection numbers of p-spin curves, Jan. 12,2022. In Silver workshop (IV): Complex geometry and related topics, International House of Japan.

    • Satsuki Oda, Nobuchika Okada, Nathan Papapietro, and Dai-suke Takahashi, “R-parity conserving U(1)x extended MSSM and its phenomenological aspects,” Progress in Particle Physics 2021 (PPP2021), Yukawa Institute for Theoretical Physics Kyoto University, 2021.09.08

    • Satsuki Oda, Nobuchika Okada, Nathan Papapietro, and Dai-suke Takahashi, “R-parity conserving U(1)x extended MSSM and its phenomenological aspects,” JPS 2021 Autumn Meeting, Online, Japan, 2021.09.16

    • Dai-suke Takahashi, “Gauge, Chiral symmetries, and Mass Generation mechanisms,” Physics Seminar, University of the Ryukyus, 2022.01.27

5. Intellectual Property Rights and Other Specific Achievements

Nothing to report

6. Meetings and Events

6.1 RIMS x OIST jointly-funded workshop: “Interactions of new trends in algebraic geometry and singularities”

October 11-15, 2021, On-line

Organizers:

  • Shiholo Ishii (University of Tokyo)
  • Hiraku Kawanoue (Chubu Univ.)
  • Tohru Omoto (Hokkaido Univ.)
  • Shinobu Hikami (OIST)

Lectures:

  • Yoshinori Gongyo (Expository, Univ. Tokyo)
  • Anne-Sophie Kaloghiros (Brunel Univ.)
  • Chen Jiang (Fudan Univ.)
  • Takehiko Yasuda (Expository, Osaka Univ.)
  • Yusuke Nakamura (Univ. of. Tokyo)
  • Victoria Hoskins (Freie Univ. Berlin)
  • Masahiko Yoshinaga (Expository, Hokkaido Univ.))
  • Takuro Abe (Kyushu Univ.)
  • Elisa Palezzato (Hokkaido Univ.)

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

Jan.11-12, 2022, International House of Japan (IHJ), Roppongi, Tokyo

Organizers:

  • Noriko Yui (Queen’s Univ.)
  • Kyoji Saito (RIMS)
  • Shinobu Hikami (OIST)

Talkers:

  • George Elliott, (Toronto Univ.)
  • Yasuyuki Kawahigashi (Univ. of Tokyo)
  • Mutsuo Oka (Tokyo Univ. of Science) 
  • Shinichi Tajima（Tsukuba Univ.）
  • Noriko Yui (Queen’s Univ.)
  • Shinobu Hikami (OIST)
  • Shihoko Ishii (Univ. of Tokyo)
  • Makiko Mase (Mannheim Univ.)

6.3 Lecture: “Elementary Particle Physics and Cosmology III (Standard Model and the Beyond)”

  • Date: Dec 02, 2021 – Jan 20, 2022 (6 lectures)
  • Venue: University of the Ryukyus
  • Lecturer: Dai-suke Takahashi (OIST)

7. Other

Nothing to report.