FY2019 Annual Report

Mathematical and Theoretical Physics Unit
Shinobu Hikami

Silver Workshop, March 2020


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 p-spin 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 d-2 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(Bose-Einstein 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 second-quantised Calogero model.
We found in particular that one of the OPE decomposition is an asymptotic series, and
the sub-exponential contribution can be interpreted as the contribution of u-channel 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 Peccei-Quinn (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 Two-Higgs Doublet Model (THDM). We utilized the state-of-the-art method to calculate vacuum decay rates at the one-loop 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 closed-form expression for the cross-channel 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 t-channel 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 4-point 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

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

  2. E. Brezin and S. Hikami, Puncture and p spin curves from matrix models,
    J. Stat. Phys. (2020) (to be published), arXiv:2001.09267.  

  3. Wenliang Li, Closed-form expression for cross-channel conformal blocks near the lightcone. J. High Energ. Phys. 2020, 55 (2020). https://doi.org/10.1007/JHEP01 (2020) 055

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

  5. Satsuki Oda, Yutaro Shoji, and Dai-suke 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)

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

  7. 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 one-time publications

Nothing to report

4.3 Oral and Poster Presentations

  1. S. Hikami, Punctures and p-spin curves from matrix models, Silver workshop 2020: Flat structure and singularities, OIST B700, March 6, 2020.
  2. S. Hikami, Ramond punctures and p-spin curves in a random matrix, December 3 2019, at workshop “Super-Riemann surfaces and related topics”, Univ. of Tokyo,Room 123.
  3. S. Hikami, Arc space, jet scheme and super conformal field theory, Workshop “Singularities and related topics” July 31,2019. Univ. of Tokyo, Room 002.
  4. S. Hikami, Singularities and moduli spaces of Riemann and Klein surfaces, Workshop “Singularities and related topics” Aug. 2, 2019. Univ. of Tokyo, Room 002.
  5. S. Hikami, Intersection theory from random supermatrices for Riemann and Klein surfaces, Mathematical condensed matter physics, RIKEN-OIST mini workshop 2019, July 5, 2019.
  6. S. Hikami, Singularity theory for the negative value p of spin curves, June 14, 2019, RIMS-OISTworkshop “On the problem of resolution of singularities and its vicinity”, OIST seaside house.
  7. H. Shimada, "Exact computation of OPE in an interacting model with space/time anisotropic scale invariance", 2019.7.5, RIKEN-OIST joint workshop “Mathematical Condensed Matter Physics”, OIST
  8. 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.
  9. H. Shimada, "M理論の定式化について" (English: "On formulation of M-theory") , 2019.11.21, Colloquium at Ryukyu University.
  10. H. Shimada, "Exact computation of OPE in an interacting model with space/time anisotropic scale invariance", 2020.1.21, Southeast University, Nanjing, China.
  11. Wenliang Li, "Closed-form expression for cross-channel conformal blocks near the lightcone", RIKEN-OIST mini Workshop 2019: Mathematical Condensed Matter Physics, OIST, Japan, 2019.07.06
  12. Wenliang Li, "Closed-form expression for cross-channel 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)
  13. Satsuki Oda, Yutaro Shoji, and Dai-suke Takahashi, “Vacuum stability in the DFSZ axion model”, Progress in Particle Physics 2019 (PPP2019), Yukawa Institute for Theoretical Physics Kyoto University, 2019.08.01
  14. Satsuki Oda, Yutaro Shoji, and Dai-suke Takahashi ,“DFSZ axion model and precise electroweak vacuum stability”, JPS 2019 Autumn Meeting, Yamagata University, 2019.09.19
  15. Satsuki Oda, Yutaro Shoji, and Dai-suke 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
  16. Satsuki Oda, Yutaro Shoji, and Dai-suke Takahashi, “High Scale Validity of the DFSZ Axion Model with Precision”, JPS 75th Annual Meeting (2020), Nagoya University, 2020.03.17
  17. Dai-suke 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:6th March 2020
  • Venue: OIST Lab3-B700 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: C016-Lab1, OIST campus
  • Speaker: Fujihiko Sugino, Institute for Basic Science, South Korea

6.3 Workshop: “Super-Riemann surfaces and related topics: joint project between OIST and University of Tokyo"

  • Date: 2019.12.2-4
  • 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 30-August 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)
    • Kei-ichi Watanabe(Nihon University)
    • Makiko Mase (Mannheim)
    • Kazuhiko Kurano (Meiji University)

6.5 OIST Symposium: "Quantum and Gravity"

  • Date:  July 23-27, 2019
  • Venue: OIST, Seaside house
  • Organizers: Reiko Toriumi(OIST) and Shinobu Hikami(OIST)

6.6 RIKEN-OIST mini Workshop 2019: Mathematical Condensed Matter Physics

  • Date: July 5-6, 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: Dai-suke 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.