# FY2018 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 spin curves and the conformal bootstrap method for three dimensions are studied. Random matrix theory is applied to biological systems.

## 1. Staff

- Prof. Shinobu Hikami, Professor
- Dr. Satsuki Oda, Staff Scientist
- Dr. Hidehiko Shimada, Staff Scientist
- Dr. Hirohiko Shimada, Postdoctoral Scholar (Until December 2018)
- Dr. Daisuke Takahashi, Visiting Researcher
- Dr. Wenliang Li, Postdoctoral Scholar
- Dr. Ayumi Kikkawa, Research Assistant (part time)
- Dr. Chika Hasegawa, Resarch Assistant (part time)
- Mr. Adrian David, PhD Student
- Ms. Shiho Saito, Research Unit Administrator
- 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 and singularity (S. Hikami)

(a) Random super matrix theory and topological invariants

We have studied the moduli space of spin curves through a random matrix theory with an external source (E. Brezin and S.Hikami, Random matrix theory with an external source, SpringerBrief in Mathematical Physics19). Finding a new formulation on the random super matrices, we have obtained new results of the topological invariants of the super moduli spaces with boundaries. ( E. Brezin and S. Hikami, Random super matrices with an external source, JHEP08(2018)086 ).

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

By the determinant bootstrap method, we studied Yang-Lee edge singularity, polymer and branched polymer, and random field Ising model. The dimensional reduction was discussed for the branched polymer and random field Ising model in the determinant method. Anderson localization for the symplectic case was also analyzed and a reasonable value of the critical exponent has been obtained.

### 3.2 String theory on AdS spacetime and aspects of quantum field theory with anisotropic scaling (Hidehiko Shimada)

Hidehiko Shimada focused on two subjects. One is on the string theory on the backgorund AdS_{5 }×*S*^{5}. Some time ago, he formulated the superspace for the background using a linear representation of the relevant supersymmetry group and imposing a quadratic constraint. This formulation has the advantage that Fermionic and the Bosonic degrees of freedom are treated on an equal footing. We are now trying to construct the Green-Schwarz type action functional of the string propagating on the background in terms of his formulation of the superspace. This is a joint work with Shota Komatsu(Princeton, IAS), in preparation.

The other subject concerns field theories with anisotropic scaling. (a) We found an interacting field theory model in 1+1 dimension with anisotropic scaling, where some 4-pt functions and OPE coefficients can be computed exactly. This is a joint work with Hirohiko Shimada (National Institute of Technology, Tsuyama College). (b) We realised that membrane worldvolume theory of M-theory actually has classical scaling symmetry which scales the time and the space coordinate differently. We are now trying to understand quantum mechanical implications.

### 3.3 Gauged U(1)’ extension of the Standard Model (S. Oda)

The Standard Model (SM) is a well-established model in describing elementary particle physics phenomena. However, the SM still suffers from several problems, such as the gauge hierarchy problem, no origin of the electroweak symmetry breaking, non-zero neutrino mass, and no candidate of the dark matter (DM). In order to solve these problems, we have investigated the minimal gauged U(1)’ extension of the SM with the classically conformal invariance, where an anomaly-free U(1)’ gauge symmetry is introduced along with a U(1)’ Higgs field and three generations of right-handed neutrinos (RHNs) for the seesaw mechanism generating neutrino masses. With no mass term allowed by the classically conformal invariance, the U(1)’ gauge symmetry is radiatively broken through the Coleman-Weinberg mechanism, which triggers the electroweak symmetry breaking. In this model, we have searched allowed parameter regions to solve the electroweak vacuum instability problem, and satisfy the Large Hadron Collider (LHC) bounds from the search for the Z’ boson resonance. We have also studied cosmological aspects of this model, the RHN DM physics, and the inflation scenario by identifying the U(1)’ Higgs boson with an inflaton. We found interesting results in which the LHC physics and cosmological observations are complementary narrowing down the model parameter space. We also study the supersymmetric version of the U(1)’ extended SM, since supersymmetric extension is a promising way to solve the gauge hierarchy problem in the SM.

### 3.4 Analytic conformal bootstrap (Wenliang Li)

In the study of conformal field theories, conformal blocks in the lightcone limit play an important role in the analytic conformal bootstrap method. In the preprint arxiv:1906.00707, I presented a compact closed-form expression for cross-channel conformal blocks in the lightcone limit, in terms of the Kampé de Fériet function. The new expression is for 4-point functions of identical scalars and applies to intermediate states of arbitrary spin and in general dimensions. Previously, compact closed-form expressions for spinning conformal blocks were only available in even dimensions. I also provided compact formulas for the Lorentzian inversion of the new expression, which will be useful for many analytic conformal bootstrap problems, such as the Wilson-Fisher fixed point, 3d Ising model, and 3d Chern-Simon-matter theories.

### 3.5 The spectral analysis of cancer gene networks (A. Kikkawa)

We have investigated the gene interaction networks in human cancer cells with the methods of random matrix theory. To characterize the cancer gene interaction networks with some specific community structures, the spectral statistics of the adjacency matrices are investigated focusing on the network localization behavior of hub nodes. A gene community is defined as a subnetwork in which the number of links between the members is larger than the number of links to the outside nodes. The hub node is the special node (gene) which has extremely large degree (links). The gene communities can be specified as sub-networks including the hub nodes. The tendency of network localization to the hub genes is parallel to the hub-dictatorship of cancer gene networks. We have found the localization of the gene interaction networks occurs when the degree of the hub is larger than a threshold value. We study specific features of the localized cancer gene communities.

## 4. Publications

### 4.1 Journals

- Hikami, Shinobu, “
*Conformal bootstrap analysis for the Yang–Lee edge singularity*”, Progress of Theoretical and Experimental Physics, https://doi.org/10.1093/ptep/pty054 (2018) - Miyazaki, Katsuhiko, Miyazaki, Kayoko W, Yamanaka, Akihiro, Tokuda, Tomoki , Tanaka, Kenji F., and Doya, Kenji, “
*Reward probability and timing uncertainty alter the effect of dorsal raphe serotonin neurons on patience*”, Nature Communications, doi.org/10.1038/s41467-018-04496-y (2018) - Shimada, Hirohiko, Takahashi, Kazutaka and Ueda, Hiroaki T., “
*Quantum interactions of topological solitons from electrodynamics*”, Physical Review B, doi.org/10.1103/PhysRevB.97.224424 - Kikkawa, Ayumi, “
*Random Matrix Analysis for Gene Interaction Networks in Cancer Cells*”, Scientific Reports, doi.org/10.1038/s41598-018-28954-1 (2018) - Brezin, Edouard and Hikami, Shinobu, “
*Random supermatrices with an external source*”, Journal of High Energy Physics, doi.org/10.1007/JHEP08(2018)086 (2018) - Tokuda, Tomoki , Yoshimoto, Junichiro , Yu, Shimizu, Okada, Go , Takamura, Masahiro , Okamoto, Yasumasa , Okamoto, Shigeto and Doya, Kenji, “
*Identification of depression subtypes and relevant brain regions using a data-driven approach*”, Scientific Reports, doi.org/10.1038/s41598-018-32521-z (2018) - Hikami, Shinobu, “
*Conformal bootstrap analysis for single and branched polymers*”, Progress of Theoretical and Experimental Physics, doi.org/10.1093/ptep/pty132 (2018) - Sudarshan Ananth, Stefano Kovacs, Yuki Sato and Hidehiko Shimada, Towards a tensionless string field theory for the N=(2,0) CFT in d=6, JHEP07(2018)135. DOI:10.1007/jhep07(2018)135

### 4.2 Books and other one-time publications

Nothing to report

### 4.3 Oral and Poster Presentations

- Shimada, Hirohiko, “
*Quantum Topological Solitons*”, Shannon unit special group seminar in honor of Prof. Oshikawa, OIST, 2018.04.18 - Shimada, Hidehiko, “
*Towards Tensionless String Field Theory for Six-dimensional (2,0) CFT*”, OIST Mathematical and Theoretical Physics Unit Seminar, OIST, 2018.06.13 - Shimada, Hidehiko, “
*Towards Tensionless String Field Theory for Six-dimensional (2,0) CFT*”, Matrix Models for Noncommutative Geometry and String Theory Workshop, Erwin Schroedinger Institute, Vienna, Austria, 2018.07.11 - Oda, Satsuki , Okada, Nobuchika, Raut, Digesh and Takahashi, Dai-suke, “
*Non-minimal Quartic Inflation in Classically Conformal U(1)' extended Standard Model*”, 26th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY2018), Barcelona, Spain, 2018.07.24 - Oda, Satsuki , Okada, Nobuchika, Papapietro, Nathan, Takahashi, Dai-suke, “
*R-parity Conserving Minimal SUSY U(1)x Model*”, 26th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY2018), Barcelona, Spain, 2018.07.24 - Hikami, Shinobu, “
*Brieskorn Singularity and Intersection Theory*”, Silver workshop, The University of Tokyo, 2018.07.27 - Shimada, Hirohiko, “
*Universal Asymptotics in One Parameter Family of OPEs*”, XIX International Congress on Mathematical Physics (ICMP2018), Montreal, Canada, 2018.07.27 - Oda, Satsuki , Okada, Nobuchika , Papapietro, Nathan and Takahashi, Dai-suke, “
*R-parity Conserving Minimal SUSY U(1)x Model*”, Progress in Particle Physics 2018 (PPP2018), 2018.08.08 - Shimada, Hirohiko, “
*Quantum Field Theory and the Land of Statistical Physics*”, Physics Colloquium, Tokai University, 2018.09.01 - Takahashi, Dai-suke, “
*Scale Invariance and Phenomenology*”, Particle and Nuclear Theory Meeting, Phenomenology of Mass Hierarchy and Planck Scale Physics Meeting, Shinshu University, 2018.09.18 - Li, Wenliang, ”
*Bootstrapping Conformal Field Theories Without Using Unitarity*”, KIAS, Seoul, South Korea, 2018.11.08 - Li, Wenliang, “
*Conformal Bootstrap Without Using Unitarity*”, OIST-Kyoto-NTU High Energy Physics Workshop 2018, OIST, 2018.11.27 - Oda, Satsuki, Okada, Nobuchika , Papapietro, Nathan, Takahashi, Dai-suke, “
*R-parity Conserving Minimal SUSY U(1)x Model*”, Shinshu University, 2018. 09.15 - Shimada, Hidehiko, “
*Splitting(-Joining) of Membranes and a 3D Analog of Riemann Surfaces*”, Workshop “Quantum Math”, OIST, 2019.02.02 - Hikami, Shinobu, “
*Hurwitz Numbers and Mirror Symmetry*”, Silver Workshop: Complex Geometry and Non-Coummutative Geometry, OIST, 2019.03.01 - Hikami, Shinobu, “
*Random Matrix Model as CFT*”, Workshop “Quantum Math”, OIST, 2019.03.03 - Oda, Satsuki, Shoji, Yutaro, Takahashi, Dai-suke, “
*Vacuum Stability in the DFSZ Axion Model*”, JPS 74th Annual Meeting, Kyushu University, 2019.03.15

## 5. Intellectual Property Rights and Other Specific Achievements

Nothing to report

## 6. Meetings and Events

### 6.1 Seminars

- One-loop tests of PM higher spin holography
- Date: Oct 2, 2018
- Venue: OIST
- Speaker: Dr. Wenliang Li (OIST)

- Towards tensionless string field theory for six-dimensional (2,0) CFT
- Date: Oct 15, 2018
- Venue: CEICO, Prague
- Speaker: Dr. Hidehiko Shimada (OIST)

- Chow ring and matrix model
- Date: Jan 28, 2019
- Venue: Nihon University
- Speaker: Prof. Shinobu Hikami (OIST)

- Elliptic solutions to BKP equation and many-body systems
- Date: Jan 30, 2019
- Venue: OIST Campus Lab1
- Speaker: Prof. Anton Zabrodin (HSE Moscow)

- Special Lecture: Modularity of Calabi-Yau Manifolds
- Date Feb 22, 2019
- Venue: OIST Campus Lab3
- Speaker: Prof. Noriko Yui (Queen’s University)

- Towards a theory of classification: general setting
- Date Feb 27, 2019
- Venue: OIST Campus, Center Building
- Speaker: Prof. George Elliott (University of Toronto)

- Topology from chaos: quantum Hall physics, Haldane conjecture and beyond
- Date: Mar 5, 2019
- Venue: OIST Campus Lab1
- Speaker: Prof. Chushun Tian (CAS Beijing)

### 6.2 Workshops & Symposium

- Silver Workshop : Complex Geometry and Related Topics
- Date: Jul 27, 2018
- Venue: Graduate School of Mathematical Sciences, University of Tokyo
- Co-Organizers: Noriko Yui (Queen’s University), Kyoji Saito (IPMU)

- OIST Mini Symposium "Holographic Tensors"
- Date: Oct 31-Nov 2, 2018
- Venue: OIST Conference Center & Seaside House
- Co-Organizers: Reiko Toriumi (OIST), Vincent Rivasseau (University Paris Sud)

- Workshop on "Hyperbolic Geometry of the Moduli Space and Related Topics."
- Dates: Jan 24-26, 2019
- Venue: Graduate School of Mathematical Sciences, University of Tokyo

- Silver Workshop: Complex Geometry and Non-Commutative Geometry
- Date: Feb 28 - Mar1, 2019
- Venue: Center Building, OIST Campus
- Co-Organizers: Noriko Yui (Queen's University), Kyoji Saito (IPMU)

- Workshop “Quantum Math”
- Date: Mar 2-3, 2019
- Venue: Lab3, OIST Campus
- Co-Organizer: Y. Kawahigashi (University of Tokyo)

## 7. Other

Nothing to report.