# Mathematical and Theoretical Physics Unit (Shinobu Hikami)

## Mathematical and Theoretical Physics Unit

#### Professor Shinobu Hikami

## Book

E. Brezin and S. Hikami,

Random Matrix Theory with an External Source,

SpringerBriefs in Mathematical Physics 19, (2016), Springer Singapore.

## Abstract

Universal behaviors can be observed in various physical phenomena. For instance, a magnet shows a phase transition with critical indices, which are determined by the symmetry and the space dimensions. They do not depend on the details of the materials. In our unit, we study the universal phenomena of the disordered systems which are typically described by random scatterings and random potentials. The random walk in Brown motion is one of the well-known problems in this field. The aim of our study is to generalize these approaches through the random matrix model and to discuss the universal phenomena.

The random matrix model can be applied to low dimensional electronic system such as a quantum dot, and also to the string theory and gauge theory. The molecular-sequence of DNA or protein seems randomly distributed, but some of these sequences can be explained by random matrix theory. The biological system is an extremely complex system. Our research project is an approach to the biological system from the mathematical and theoretical physics by the use of the random matrix theory.

## Upcoming Events

## Past Events

**Symposium: Bootstrap Approach to Conformal Field Theories and Applications**

Scale invariant theories, i.e. theories which look the same at all distance and energy scales, play an important role in physics. Through Wilson’s renormalization group, scale invariant theories arise naturally in phase transitions. They are also the bread and butter of current thinking about particle physics beyond the Standard Model. These theories usually possess an emergent symmetry, conformal invariance, and are hence referred to as `Conformal Field Theories’ (CFTs). The quest to classify and solve CFTs is a major goal of theoretical physics. Recently, this quest has received a strong boost with the development of the ‘conformal bootstrap’ technique. This workshop will bring together two groups of researchers: theorists working on the conformal bootstrap and on formal aspects of CFTs, and condensed-matter and statistical theoretical physicists working on the concrete examples of systems exhibiting phase transitions described by CFTs. The goal will be to inform about the most important theoretical and practical developments in the conformal bootstrap, and about the most urgent questions relevant for condensed matter and statistical physics which can be addressed using conformal bootstrap.

- Organizers: Slava Rychkov and Shinobu Hikami
- Date: March 19-23, 2018
- Venue: Conference Center, OIST
- Invited Speakers:
- Luis Fernando Alday (Oxford)
- Nando Gliozzi (Torino)
- Rajesh Gopakumar (ICTS-TIFR)
- Sean Hartnoll (Stanford)
- Shinobu Hikami (OIST)(organizer)
- Yu Nakayama (Rikkyo)
- Silviu Pufu (Princeton)
- Leonard Rastelli (SUNY)
- Slava Rychkov (ENS, CERN)(organizer)
- Aninda Sinha (IIS, Bangalore)
- Satoshi Yamaguchi (Osaka)
- Masahito Yamazaki (IPMU,Tokyo)

**RIKEN-Osaka-OIST Joint Workshop 2018**

- Organizers: :Koji Hashimoto (Osaka), Yoshimasa Hidaka (RIKEN), Hirohiko Shimada (OIST), Sotaro Sugishita (Main) (Osaka)
- Date: March 12-14, 2018
- Venue: B250 (Mar 12 & 13), C209 (Mar 14), OIST

**Symposium:**

The moduli space of compact Riemann surfaces, the space of all biholomorphism classes of compact Riemann surfaces, is one of the most attractive subjects in mathematics. Nowadays it firmly combines mathematical physics and integrable systems with low-dimensional topology including hyperbolic geometry of surfaces, which induces the Weil-Petersson symplectic structure on the space. In particular, the topological recursion by Eynard and Orantin generalizing Mirzakhani's recursive formula for the Weil-Petersson volume has some strong influence in various research areas.

In this workshop, we will read intensively some research papers on the symplectic structure of the moduli space and related topics, and will have some talks on original researches. This workshop is supported by a joint project between the OIST and the University of Tokyo.

This workshop is supported by a joint project between the OIST and the University of Tokyo.

- Date: January 26 (Friday) - 28 (Sunday), 2018
- Venue: Room 123, Graduate School of Mathematical Sciences Bldg., University of Tokyo (Komaba Campus).
- Organizers: Y. Tadokoro (Kisarazu), T. Sakasai (Univ. Tokyo) and N. Kawazumi (Univ. Tokyo)

**MINI SYMPOSIUM: New development in Teichmuller space theory ; MCM2017**

Theory of Teichmuller space has a long history for the moduli space of Riemann surface. Recently beyond classical Teichmuller space research, new extended concept and technique are developed and they are important for various areas of mathematical physics. Particularly higher Teichmuller space attracts interest, which concerns SL(n,R) geometry and its boundary. In this mini symposium, we concentrate on the new concept and technique and discuss from wide point of view of topology, physics and integrable systems. For examples, the cluster algebra and open intersection numbers are discussed closely. We intend to develop a theory for new structure of Teichmuller space in a new direction of mathematical physics.

- Date:
- Venue: C210, Center Building, OIST
- Organizers: Nariya Kawazumi (Univ. of Tokyo), Takuya Sakasai (Univ. of Tokyo), Shinobu Hikami (OIST)
- Invited talkers:
- A. Alekseev, Geneve Univ.
- R. Inoue, Chiba Univ.
- R. Kashaev, Geneve Univ.
- T. Kitayama, Univ. of Tokyo
- A. Kuniba, Univ. of Tokyo
- A. Tsvietkova, OIST

- Program: PDF
- Photo: JPEG

**Seminar:**

- Date: Thursday, November 9, 2017
- Time: 13:30 - 14:30
- Venue: Room 056, Graduate School of Mathematical Sciences Bldg., University of Tokyo (Komaba Campus). Seminar via TV conference system in Room B611 (Lab2) , OIST.
- Speaker: Prof. Edouard Brezin (lpt ens, Paris)

Title: "Various applications of supersymmetry in statistical physics".

Abstract: Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.

**Workshop: MSRI Summer Graduate School – Commutative Algebra and Related Topics**

The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research. The lecturers will give topics courses and then the graduate students will meet in small groups and challenge problems and have discussion sessions related to each topic.

- Date:
- Venue: OIST Seaside House (May 23 at Conference Center, OIST Campus)
- Organizers: Shihoko Ishii (TWCU), Kazuhiko Kurano (Meiji), Ken-ichi Yoshida (Nihon), Shinobu Hikami (OIST)
- Lecturers:
- David Eisenbud (MSRI / University of California)
- Claudia Polini (University of Notre Dame)
- Claudiu Raicu (University of Notre Dame)
- Shunsuke Takagi (University of Tokyo)
- Ryo Takahashi (Nagoya University)

- Program:
- Photo: jpg

**Symposium: Geometry of Quadratic Differentials and Related Topics**

Quadratic differentials, meromorphic tensor fields on Riemann surfaces of some special type, have been studied classically in hyperbolic geometry and complex analysis. Recently it has been clarified that low-dimensional topology including hyperbolic geometry of surfaces is closely related to mathematical physics and integrable systems. This can be illustrated by the topological recursion by Eynard and Orantin generalizing computation of the Weil-Petersson volume of the moduli space of Riemann surfaces, whose influence one can find in various research areas. Accordingly quadratic differentials are playing some important roles also in mathematical physics and integrable systems. In this workshop, we will read intensively some research papers on the geometry of quadratic differentials and related topics, and will have some talks on original researches. This workshop is supported by a joint project between the OIST and the University of Tokyo.

- Organizers: Y. Tadokoro (Kisarazu), T. Sakasai (Univ. Tokyo) and N. Kawasumi (Univ. Tokyo)
- Date: January 11-13, 2017
- Venue: University of Tokyo, Komaba, Mathematical Science Building #002 Info (in Japanese)

**Pre-Conference MCM2016 at Tokyo**

- Date: October 20-22, 2016
- Venue: University of Tokyo, Komaba, Mathematical Science Building
- Organizers: Nariya Kawazumi(Univ. Tokyo), Shinobu Hikami(OIST)
- Program & Abstracts

**Workshop: Moduli space, conformal field theory and matrix models; MCM2016**

- Date: October 24-27, 2016
- Venue: C209, OIST
- Organizers: Nariya Kawazumi(Univ. Tokyo), Shinobu Hikami(OIST)
- Program & Abstracts
- Group Photo

**TSUDA COLLEGE AND OIST JOINT WORKSHOP ONCALABI–YAU VARIETIES:ARITHMETIC, GEOMETRY AND PHYSICS **

- Date: August 1–3, 2016
- Venue: August 1–2 at Tsuda College Room 7309, August 3 at Tokyo University Komaba Campus Room 117
- Organizers: Noriko Yui (Queen’s University) and Takayuki Oda (OIST)
- Program (PDF) & Abstracts (PDF)

**"OIST-iTHES-CTSR 2016" International Workshop**

- Date: Friday 8 - Monday 11 July, 2016
- Venue: Fri 8th (B250), Sat 9th (C209), Mon 11th (B250)
- Organizers: RIKEN iTHES, OSAKA CTSR, and OIST (Theoretical Units)

**Seminar:**

- Date: Thursday, July 7, 2016
- Time: 15:00 - 16:00
- Venue: C209, Center Building, OIST
- Speaker: Prof. Jean Zinn-Justin (CEA Saclay)

**Title**: 3D field theories with Chern-Simons term for large N in the Weyl gauge

**Abstract:** ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.

We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.

We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.

Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.

**Seminar: **

- Date: Wednesday, March 30, 2016
- Time: 11:00 - 12:00
- Venue: C209, OIST
- Speaker: Prof. Katsuya Shimizu（Osaka University）

**Title**: 200-K superconductivity in compressed hydrogen sulfide systems

**Abstract: **After finding superconductivity in 100 years ago, "room-temperature"superconductor has been long-fascinated target for physicists. Superconductivity above 200K was recently reported in the highly compressed hydrogen sulfide (H2S) by Drozdov et al1. The crystal structure of the superconducting sulfur hydride systems was studied by using the synchrotron x-ray diffraction at room temperature and the superconducting temperature. H2S and D2S were compressed to 150 GPa in DAC with same process with Drozdov et al1, and cooled down to 10 K in the cryostat in the x-ray diffractometer in SPring-8. The resistivity was onitored at all cooling process. The critical temperature and zero resistivity were observed around 180 K, and the collected x-ray diffraction data showed good agreement with the theoretically predicted structures of R3m and Im-3m2. No structural difference was observed between at 10 K and room temperature. The creation of the high-temperature superconductor was experimentally also confirmed by our Osaka group. H2S gas was cooled down to around 200 K and liquefied then compressed up to 150 GPa in a diamond-anvil cell (DAC). The resistance decreased with increasing pressure and showed metallic behavior in cooling process. The superconducting transition was observed at 60-70 K with zero resistance. At the second cooling after warmed up to room temperature, the resistance dropped to zero from 180 K.

This work was supported by JSPS KAKENHI Grant Number 26000006 and the European Research Council 2010-Advanced Grant 267777.

References:

[1] A. Drozdov et al., Nature 525 73 (2015).

[2] D. Duan et al., Scientific Reports 4, 6968 (2014).

**Seminar: **

- Date: Friday, December 25, 2015
- Time: 11:00 - 12:00
- Venue: C015, Lab1, OIST
- Speaker: Prof. Yasutomo J. Uemura （Columbia University）

**Title**: BEC to BCS crossover picture for high-Tc cuprate and unconventional superconductors, and pairing due to comparable spin-charge energy scales: message from muons and neutrons

**Abstract:** Soon after the discovery of high-Tc superconductors in 1986, we started muon spin relaxation (MuSR) measurements of the magnetic field penetration depth, and demonstrated nearly linear correlations between Tc and the superfluid density n_{s}/m^{*}, which are manifest not only in cuprates but also in many other unconventional superconductors including Alkali doped C60, FeAs and some of the heavy-fermion systems . The strong dependence of Tc on carrier density is not expected in the BCS condensation, but is a main characteristic of Bose Einstein Condensation. Another important scaling of Tc is seen with the energy of the magnetic resonance mode measured by neutron scattering, which can be viewed as a spin–charge soft mode related to competing antiferromagnetic state, analogous to rotons in superfluid He related to competing solid HCP phase. This roton-like scaling is expected when condensed bosons are excited with phase fluctuations to another bosonic state, without pair breaking. This again is different from pair-breaking excitations across the energy gap in BCS condensation. We discuss these features and adopting BEC-BCS crossover picture for the cuprates, which I proposed in 1994 . Further analyses of the Tc-superfluid density (charge energy) scaling and Tc-spin wave energy (mediating boson energy) correlations lead to a possible pairing mechanism based on comparable spin and charge energy scales and dynamic synchronized charge motion in “traffic-light resonance”

References:

[1] Y.J. Uemura et al., Universal Correlations between Tc and ns/m∗ (Carrier Density over Effective Mass) in High-Tc Cuprate Superconductors, Phys. Rev. Lett. 62 (1989) 2317-2320.

[2] Y.J. Uemura et al., Basic Similarities among Cuprate, Bismuthate, Organic, Chevrel Phase, and Heavy-Fermion Superconductors Shown by Penetration Depth Measurements, Phys. Rev. Lett. 66 (1991) 2665-2668.

[3] Y.J. Uemura, Superconductivity: Exotic Commonalities in Phase and Mode, Nature Materials 8 (2009) 253-255.

[4] Y.J. Uemura, Energy Scales of Exotic Superconductors, an invited talk presented at the International Workshop on Polarons and Bipolarons in High-Tc Superconductors and Related Materials,Cambridge, UK, April, 1994, in Polarons and Bipolarons in High-Tc Superconductors and Related Materials, ed. by E. Salje, A.S. Alexandrov and Y. Liang, Cambridge University Press (1995), p.p.453-460.

[5] Y.J. Uemura, Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors (Plenary Talk at SCES2008, Buzios, Brazil, Aug., 2008), Physica B404 (2009) 3195-3201.

#### Workshop on "Moduli spaces of abelian varieties and curves, and related analysis"

- Dates: December 15-18, 2015
- Venue : Graduate School of Mathematical Sciences, The Univ. of Tokyo (@Komaba Campus)
- Program: PDF

#### RMT2015: Random matrix theory from fundamental mathematics to biological applications

- Date: Monday, November 2- Friday, November 6, 2015
- Venue: C209, OIST
- Schedule, Title and Abstract: PDF
- Slides

**Seminar: **

- Date: Friday, November 20, 2015
- Time: 11:00-12:00
- Venue: C016, Lab1, OIST
**S**peaker: Tsunehide Kuroki (Kagawa Kosen)

**Title**: Spontaneous supersymmetry breaking in matrix model and superstring theory

**Abstract:** We show that a supersymmetric matrix model is a promising candidate for the first example of nonperturbative definition of superstring theory. We prove that in this model, the supersymmetry is preserved in all orders in perturbation theory in the 1/N expansion, but that it gets broken nonperturbatively and spontaneously. We observe that this breaking is triggered by an instanton in the matrix model. We also present quite recent results of correlation functions in the matrix model in all orders of the 1/N expansion by using the random matrix theory. These results convince us that the matrix model is a string theory.

**MCM2015 Autumn: **

- Date: Thursday, October 29 and Friday, October 30, 2015
- Venue: Komaba, University of Tokyo, Math. Dep. Room 002.
- Schedule:
- October 29th (Thursday)
- 10:00-11:00 Hikami
- 11:30-12:30 Andersen
- 14:30-15:30 Sakasai
- 16:00-17:00 Hayata
- 18:00- Dinner at Komaba

- October 30th (Friday)
- 10:00-11:00 Murakami
- 11:30-12:30 Zinn-Justin
- 14:30-15:30 Kuno
- 16:00-17:00 Shimada

- October 29th (Thursday)

- Title and Abstract: PDF

**Seminar: **

- Date: Wednesday, May 27th, 2015
- Time: 13:00-14:00
- Venue: C016, Lab1, OIST

Speaker: Dr. Serguei Brazovskii from CNRS & University Paris-Sud, Orsay, France

**Title**: Solitons in low dimensional electronic systems of synthetic conductors.

**Abstract:** A vast variety and whole families of “synthetic conductors” have been designed by motivation and for the purpose of obtaining desired electronic and optical properties. A firework of new physical effects of electronic correlations feeds fundamental experimental and theoretical researches. Diverse phase transitions are commonly observed towards various electronic phases: superconductivity, anti-ferromagnetism, ferroelectricity, charge order, charge- and spin density waves, Mott and Peierls insulators, phases induced by high magnetic and electric fields and by optical pumping. Vulnerability of the broken symmetries gives rise to topological defects like electronic vortices, walls, stripes. The typical low-dimensional architecture of these compounds brings these objects to a microscopic scale giving rise to “solitons” which description will be the major content of this talk. The solitons are self-localized configurations which shapes explore the ground state degeneracy. The mathematics of exact solutions for many-body models relates these trajectories to profiles of waves’ arrays and of superwaves in the ocean and to pulses in optical fibers. The solitons can be the lowest energy optical excitations or the carriers of charge or/and spins, taking these functions from conventional electrons. The “instantons” appear as processes of dynamic conversion of normal electrons into solitons. In a broad class of strongly correlated systems, beyond the low-dimensionality, the solitons can persist acquiring forms of more complicated topological excitations which give incarnations to long time searched “spinons” and "holons"

**Host:** Prof. Shinobu Hikami

**Seminar: **

- Date: Wednesday, June 3, 2015
- Time: 13:00-14:00
- Venue: C016, Lab1, OIST
- Speaker: Dr. Natasha Kirova from CNRS & University Paris-Sud, Orsay, France

**Title**: Electronic ferroelectricity in carbon-based systems: from reality of organic conductors to promises of polymers

**Abstract:** All families of carbon based materials – graphite, graphene, nanotubes, fullerenes and a vast multitude of conjugated polymers and organic crystals – are promising electronically and optically active substances. Recently a new perspective has been added to their researches: an electronic ferroelectricity. Ferroelectrics are exploited as active gate materials, in capacitors, electro-optical-acoustic modulators, in WiFi devices, in perspective RAM. Flexible lightweight carbon ferroelectrics are desired as ultrasound sensors in medical imaging. The super-polarisable state of “the ferroelectric Mott semiconductor” was discovered (Grenoble-Orsay-Moscow) in conducting organic stacks. Less conducting ferroelectrics complexes with neutral-ionic transitions (Tokyo-Tsukuba) became the objects of studies by advanced femto-second and tera-Hz optics (Tokyo). The principle novelty of organic ferroelectrics is that the polarization comes from electronic ordering rather than from ionic displacements. The microscopic design of all new materials is based on coexisting symmetry lowering effects: the dimerization of bonds and the dimerization of sites. With this forecast we could indicate the class of conducting polymers where the ferroelectricity should be present. The theory predicted an existence of solitons (which might have been already observed in Utah experiments on Kyoto materials) with non-integer variable charges, which are the walls separating domains with opposite electric polarisations. Their physics will serve to relate transient ferroelectric processes and the visible range optics. The same symmetry principle applies also to zigzag edges of graphene nano-ribbons which can be tested for the ferroelectricity.

**Host:** Prof. Shinobu Hikami

#### RIKEN-Osaka-OIST-Taiwan mathphys workshop

- Date: March 2-4, 2015
- Venue: OIST Main Campus, B503, Lab.1

**Seminar: **

- Date: March 5, 2015 10:00 am-11:00 am
- Venue: C016, Lab1, OIST
- Speaker: Dr. Tatsuo Azeyanagi (LPTENS, Paris)

**Title**: Anomalies, Chern-Simons Terms and Black Hole Entropy

**Abstract: ** Quantum anomalies enable us to access to some important information about quantum field theories in a robust way. Recently, the hydrodynamic limit of the systems with the anomalies has been actively investigated, together with its dual holographic description by gravitational theories with Chern-Simons terms. In this presentation, I will start with a review on the effect of the anomalies in the hydrodynamic limit of conformal field theories. Then I would like to explain how the beautiful property of Chern-Simons terms helps us to compute in detail various quantities relevant to the anomalies through the dual gravitational description. I will also discuss the implication of our analysis to microscopic counting of black hole entropy in higher dimensions.

Topotronics2015: The 1st International Workshop on the Topological Electronics, OIST B250, March 9-11, 2015

MCM2015: Moduli Space, Conformal Field Theory and Matrix Model, OIST C209, March 16-18, 2015

Program, Titles and Abstracts of the Talks (PDF)

The slide files (PDF) are listed HERE. You need the password in order to open these files.

RMT2013 Fluctuations of Complex Systerms, OIST Seaside House & C209, Oct 27 - Nov 1, 2013

JIBW 3rd Japan-Israel Binational Workshop on Quantum Phenomena, OIST Seaside House, March 10-13, 2013

RMT2012 :OIST Spring Course on Random Matrix Theory for Complex Systems OIST Seaside House, April 15-21, 2012