FY2019 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. 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
 Dr. Daisuke Takahashi, Visiting Researcher
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 supersymmetry (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. The spin structure of this moduli space is extended to the half integer spin p=1/2+ n. The intersection numbers for such half integer spin is studied. This is related to the Ramond punctures on the Riemann surfaces. (E. Brezin and S. Hikami, Punctures and pspin curves from matrix models, arXiv:2001.09267).
(b) Bootstrap analysis for random magnetic field Ising model
By the determinant bootstrap method, we studied a random field Ising model. The dimensional reduction was discussed for the branched polymer and random field Ising model in the determinant method. We find the dimensional reduction of the d dimensional random magnetic field to pure Ising model in d2 dimension does not work under 5 dimensions. (S.Hikami,PTEP 2019, 8 (2019) 083A03).
3.2 String theory on AdS spacetime and aspects of quantum field theory with anisotropic scaling (Hidehiko Shimada)
I have worked on two topics.
(1) Together with Masanori Hanada(Southampton University) and Nico Wintergerst (Niels Bohr Institute),
we pointed out that the colour confinement phenomena and the BEC(BoseEinstein Condensation)
can be thought as the same phenomena, the only difference being that of the gauge group.
(2) Together with Hirohiko Shimada (National Institute of Technology, Tsuyama College),
we continued our study of exact computation of OPE in the secondquantised Calogero model.
We found in particular that one of the OPE decomposition is an asymptotic series, and
the subexponential contribution can be interpreted as the contribution of uchannel OPE.
3.3 Extended models of the Standard Model and electroweak vacuum stability (S. Oda, D.s. Takahashi)
The observed Higgs boson mass (125 GeV) at the LHC (Large Hadron Collider) indicates that the electroweak vacuum is unstable in the Standard Model (SM). Also, the SM suffers from other several problems, such as 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, where a new PecceiQuinn (PQ) symmetry is introduced along with an additional Higgs doublet field and a PQ complex scalar one to the SM. In this model, since the PQ field couples very weakly, an effective theory of our model can be reduced to the TwoHiggs Doublet Model (THDM). We utilized the stateoftheart method to calculate vacuum decay rates at the oneloop level, and found that the conditions of the vacuum stability and the absence of Landau poles are stringently complementary narrowing down the model parameter space (S. Oda, Y. Shoji, and D.s. Takahashi, JHEP03(2020)011). We also study the supersymmetric version of the gauged U(1)’ extension of the SM, since supersymmetric extension is a promising way to solve the gauge hierarchy problem in the SM.
3.4 Analytic conformal bootstrap (Wenliang Li)
Conformal blocks are central to the bootstrap approach to conformal field theories. They play a crucial role as the building blocks for the nontrivial bootstrap equation, which can be studied more analytically near the lightcone. Previously, a general closedform expression for the crosschannel conformal blocks in the lightcone limit was found. In a more recent work (arxiv: 1912.01168), the analytic expressions for conformal blocks were extended to all orders both in the s and tchannel lightcone expansions. The new analytic formulae apply to intermediate operators of arbitrary spin and in general spacetime dimensions. Before this work, the general lightcone expansions of 4point scalar conformal blocks were only known in d=2,4,6 dimensions. We are now applying the new analytic formulae to concrete models outside even spacetime dimensions.
3.5 The spectral analysis of cancer gene networks (A. Kikkawa)
We investigated the gene interaction networks in human cancer cells. For the purpose of characterizing the cancer gene networks with some specific community structures, the spectral statistics of the adjacency matrices are studied. The node degree correlation function shows the disassortative behavior in the large degrees, so the hub nodes show tendencies to link to small degree nodes.
4. Publications
4.1 Journals

S. Hikami, Dimensional reduction by conformal bootstrap, Prog. Theor. Exper. Phys. 2019 (2019) 083A03. https://doi.org/10.1093/ptep/ptz081

E. Brezin and S. Hikami, Puncture and p spin curves from matrix models,
J. Stat. Phys. (2020) (to be published), arXiv:2001.09267. 
Wenliang Li, Closedform expression for crosschannel conformal blocks near the lightcone. J. High Energ. Phys. 2020, 55 (2020). https://doi.org/10.1007/JHEP01 (2020) 055

Wenliang Li, Lightcone expansions of conformal blocks in closed form, J. High Energ. Phys. (2020) (to be published), arxiv: 1912.01168 .

Satsuki Oda, Yutaro Shoji, and Daisuke Takahashi, “High scale validity of the DFSZ axion model with precision”, Journal of High Energy Physics, JHEP 03 (2020) 011, DOI: 10.1007/JHEP03(2020)011 (2020)

H. Shimada, Masanori Hanada and Nico Wintergerst, "Color Confinement and BoseEinstein Condensation", a preprint submitted to Sci. Post., arxiv:2001.10459

Ayumi Kikkawa, Spectral analysis for gene communities in cancer cells, Journal of Complex Networks, Volume 8, Issue 1, (2020), cnaa005, https://doi.org/10.1093/comnet/cnaa005
4.2 Books and other onetime publications
Nothing to report
4.3 Oral and Poster Presentations
 S. Hikami, Punctures and pspin curves from matrix models, Silver workshop 2020: Flat structure and singularities, OIST B700, March 6, 2020.
 S. Hikami, Ramond punctures and pspin curves in a random matrix, December 3 2019, at workshop “SuperRiemann surfaces and related topics”, Univ. of Tokyo,Room 123.
 S. Hikami, Arc space, jet scheme and super conformal field theory, Workshop “Singularities and related topics” July 31,2019. Univ. of Tokyo, Room 002.
 S. Hikami, Singularities and moduli spaces of Riemann and Klein surfaces, Workshop “Singularities and related topics” Aug. 2, 2019. Univ. of Tokyo, Room 002.
 S. Hikami, Intersection theory from random supermatrices for Riemann and Klein surfaces, Mathematical condensed matter physics, RIKENOIST mini workshop 2019, July 5, 2019.
 S. Hikami, Singularity theory for the negative value p of spin curves, June 14, 2019, RIMSOISTworkshop “On the problem of resolution of singularities and its vicinity”, OIST seaside house.
 H. Shimada, "Exact computation of OPE in an interacting model with space/time anisotropic scale invariance", 2019.7.5, RIKENOIST joint workshop “Mathematical Condensed Matter Physics”, OIST
 H. Shimada, "Exact computation of OPE in an interacting model with space/time anisotropic scale invariance", 2019.9.17, The Physical Society of Japan 2019 Autumn Meeting, Yamagata Univ.
 H. Shimada, "M理論の定式化について" (English: "On formulation of Mtheory") , 2019.11.21, Colloquium at Ryukyu University.
 H. Shimada, "Exact computation of OPE in an interacting model with space/time anisotropic scale invariance", 2020.1.21, Southeast University, Nanjing, China.
 Wenliang Li, "Closedform expression for crosschannel conformal blocks near the lightcone", RIKENOIST mini Workshop 2019: Mathematical Condensed Matter Physics, OIST, Japan, 2019.07.06
 Wenliang Li, "Closedform expression for crosschannel conformal blocks near the lightcone", The 14th Kavli Asian Winter School on Strings, Particles and Cosmology, Tohoku University, Japan, 2020.01.18 (gong show + poster presentation)
 Satsuki Oda, Yutaro Shoji, and Daisuke Takahashi, “Vacuum stability in the DFSZ axion model”, Progress in Particle Physics 2019 (PPP2019), Yukawa Institute for Theoretical Physics Kyoto University, 2019.08.01
 Satsuki Oda, Yutaro Shoji, and Daisuke Takahashi ,“DFSZ axion model and precise electroweak vacuum stability”, JPS 2019 Autumn Meeting, Yamagata University, 2019.09.19
 Satsuki Oda, Yutaro Shoji, and Daisuke Takahashi, “High Scale Validity of the DFSZ Axion Model with Precision”, Program for the 27th Regular Meeting of the New Higgs Working Group, Osaka University, 2019.12.13
 Satsuki Oda, Yutaro Shoji, and Daisuke Takahashi, “High Scale Validity of the DFSZ Axion Model with Precision”, JPS 75th Annual Meeting (2020), Nagoya University, 2020.03.17
 Daisuke Takahashi, “Reconsideration and Extension of the standard model based on collider physics and cosmological observations, Physics Seminar, University of the Ryukyus, 2020.01.30
5. Intellectual Property Rights and Other Specific Achievements
Nothing to report
6. Meetings and Events
6.1 Silver workshop 2020 : Flat Structure and Singularities
 Date：6^{th} March 2020
 Venue： OIST Lab3B700 and B711
 Invited speakers：
 Kyoji Saito（IPMU）
 Kostantin Aleshkin (Columbia Univ.)
 Mitsuo Kato (Ryukyu Univ.)
 Yoshihisa Saito (Rikkyo Univ.)
 Shinichi Tajima （Niigata Univ.）
 Motoko Kato (Ehime Univ.)
 Shinobu Hikami (OIST)
6.2 Seminar: "Study of highly entangled quantum spin chains"
 Date: Thursday, February 6th, 2020
 Venue: C016Lab1, OIST campus
 Speaker: Fujihiko Sugino, Institute for Basic Science, South Korea
6.3 Workshop: “SuperRiemann surfaces and related topics: joint project between OIST and University of Tokyo"
 Date: 2019.12.24
 Venue: University of Tokyo,Graduate school of mathematical sciences
(December 2,3: Room 123, December 4: Room 128).  Organizers:
 Nariya Kawazumi (Univ. of Tokyo)
 Takuya Sakasai(University of Tokyo
 Shinobu Hikami(OIST)
 Speakers:
 Yusuke Kuno (Tsuda University)
 Anton Zeitlin (Louisiana State University)
 Casey Blacker (East China Normal University)
 Shinobu Hikami(OIST)
 Motoko Kato (EhimeUniversity)
6.4 Workshop: "Singularities and related topics"
 Date: July 30August 2, 2019
 Venue: The University of Tokyo (Komaba),Room 002.
 Invited Speakers:
 Anne Moreau(Lille)
 Claus Hertling(Mannheim)
 Shihoko Ishii(The University of Tokyo/Tsinghua University)
 Masataka Tomari(Nihon University)
 Keiichi Watanabe(Nihon University)
 Makiko Mase (Mannheim)
 Kazuhiko Kurano (Meiji University)
(others)
6.5 OIST Symposium: "Quantum and Gravity"
 Date: July 2327, 2019
 Venue: OIST, Seaside house
 Organizers: Reiko Toriumi(OIST) and Shinobu Hikami(OIST)
6.6 RIKENOIST mini Workshop 2019: Mathematical Condensed Matter Physics
 Date: July 56, 2019
 Venue: B250, Center Building, OIST
 Organizers:
 Masahiro Nozaki (RIKEN) Chair person
 Masaru Hongo (Keio Univ./RIKEN)
 Kanato Goto (RIKEN)
 Hidehiko Shimada (OIST)
6.7 RIMS x OIST Workshop: “On the problem of resolution of singularities and its vicinity”
 Date: June 10  June 14, 2019
 Venue: Seaside house (OIST)
 Organizers:
 K. Matsuki (Purdue Univ.)
 H. Kawanoue (Chubu Univ.)
 S. Ishii (Univ. of Tokyo/Tsinghua Univ.)
 T. Yasuda (Tohoku Univ.)
 S. Hikami (OIST)
6.8 Workshop: "Johnson homomorphisms and related topics 2019"
 Date: May 13 – 17, 2019
 Venue: The University of Tokyo, Lecture Hall of the Mathematical Science Building
 Organizers:
 Shinobu Hikami
 Nariya Kawazumi
 Gwenael Massuyeau
 Hiroaki Nakamura
 Takuya Sakasai
 Christine Vespa
6.9 Lecture: "Particle Physics and Cosmology – Standard Model and Physics beyond the Standard Model – "
 Date: Nov 28, 2019 – Jan 23, 2020 (6 lectures)
 Venue: University of the Ryukyus
 Lecturer: Daisuke Takahashi (OIST)
6.10 Seminar: "Subaru weak lensing Survey of Dark Matter Subhalos in nearby clusters of galaxies"
 Date: May 30, 2019
 Venue: OIST Campus Lab1
 Speaker: Toshifumi Futamase (Kyoto Sangyo University)
6.11 Seminar:"Bounce Configuration from Gradient Flow"
 Date: Feb 25, 2020
 Venue: OIST Campus Lab1
 Speaker: Yutaro Shoji, KMI (Nagoya University)
7. Other
Nothing to report.