Matrix Model for Superstring/M-theory

Dec 1, 2025, 9:55 AM → Dec 5, 2025, 1:00 PM Asia/Tokyo

Yukawa Institute for Theoretical Physics, Kyoto University

Overview

Matrix models are excellent frameworks for non-perturbative formulation of string theory and M-theory and expected to play an essential role in understanding the holographic principle. This workshop focuses on such matrix models, especially on the BFSS, IKKT and BMN matrix models, and also on other related topics regarding recent developments in understanding of holography and numerical methods. The topics include

1. Revisit to the holography from modern perspectives
2. Application of numerical methods (Monte Carlo methods, bootstrapping, quantum simulation, ...)
3. Black holes realized in finite-temperature matrix models
4. Other low-dimensional theory and its holography (JT gravity and SYK model, ...)

This workshop is organized in the spirit of "Matrix Quantum Mechanics for M-theory Revisited" (CERN, January 8–12, 2024).

No online streaming will be provided in this workshop.
While presentations will be limited to invited talks, we plan to include discussion sessions (intended as a panel discussion format), informal lectures and a poster session.

Invited Speakers

Yiming Chen (Stanford University) 
Sean Hartnoll (University of Cambridge) 
Goro Ishiki (University of Tsukuba) 
Hikaru Kawai (National Taiwan University) 
Edward Mazenc (ETH Zurich) 
Harish Murali (Perimeter Institute) 
Jun Nishimura (KEK, Sokendai) 
Denjoe O'Connor (Dublin Institute for Advanced Studies) 
Enrico Rinaldi (Quantinuum, RIKEN) 
Victor Rodriguez (UC Santa Barbara)
Shigeki Sugimoto (Kyoto University)
Seiji Terashima (YITP, Kyoto University)
Ziqi Yan (Niels Bohr Institute) 
Zechuan Zheng (Perimeter Institute)
 

Organizers

Yuhma Asano (University of Tsukuba)      
Masanori Hanada (Queen Mary University of London)      
Etsuko Itou (YITP, Kyoto University)      
Shota Komatsu (CERN)      
Hidehiko Shimada (National Institute of Technology, Akashi College)      
Hiromasa Watanabe (Keio University)

Monday, December 1

Opening

Session

1 Fortuity with a single matrix

It has recently been proposed that supersymmetric black hole microstates exhibit “fortuity”: their very existence depends sensitively on the finite, precise values of N, the number of degrees of freedom in the dual theory. In this talk, after reviewing the core ideas of fortuity in both large-N gauge theories and toy models such as the SYK model, I will describe a simple matrix quantum-mechanical model containing a single adjoint fermion. I will show that the model is exactly solvable while containing many fortuitous states. Using the model, I will sketch how properties of fortuity - particularly the sensitivity to N - can be seen using techniques such as the unitary matrix integral. The talk will be based on arXiv:2511.00790.

Speaker: Yiming Chen

Fortuity with a single matrix_Kyoto.pdf

Coffee break

Session

2 Universality of Heavy Operators in Matrix Models

In large N theories with a gravity dual, generic heavy operators should be dual to black holes in the bulk. The microscopic details of such operators should then be irrelevant in the low energy theory. I will talk about a simple two matrix model -- the Hoppe model -- which also exhibits universality. Using analytics as well as Monte Carlo simulations, I will show that there exists a universal black hole regime where the eigenvalue densities are given by universal parabolas and the correlation functions of probes in these backgrounds are completely determined by a few parameters. The talk will be based on this paper arXiv:2507.21207

Speaker: Harish Murali

talkKyoto.pdf

Lunch

Session

3 On the landscape of minimal string theories and multi-matrix duals

I will review recent progress in charting the landscape of two-dimensional (minimal) string theories. This includes novel developments such as the Virasoro minimal string and the complex Liouville string, as well as revisiting the older ADE minimal string models. I will discuss their worldsheet descriptions, their matrix-model duals, and prospects for further directions and generalizations. If time permits, I will present a gluing formula for conformal boundaries and comment on possible extensions to higher-dimensional string theories.

Speaker: Victor Rodriguez

2025Nov_VictorRodriguez_OnMinimalStringLandscape_YITP_slides.pdf

Coffee break

Discussion session

Free discussion

Informal lecture: Overview of matrix models

4 Review on matrix models

Speaker: Yuhma Asano

Overview_of_matrix_models_YITP.pdf

Tuesday, December 2

Session

5 The polarised IKKT model

The IKKT model is a large N matrix integral that arises in string theory as the worldvolume theory of N D-instantons. It holds the promise of being a uniquely tractable model of holographic duality, but has some important differences with other better-understood cases, notably the absence of a time and the related absence of a "decoupling limit” in which the theory is obtained as an isolated sub-sector of string theory. I will discuss a supersymmetric deformation of the IKKT model that may improve the situation by introducing a dimensionless coupling constant. Supersymmetric localisation allows the model to be greatly simplified. I will discuss the phase diagram of the model, which exhibits a phase transition between two limits, and the sense in which the model leads to an emergent spacetime.

Speaker: Sean Hartnoll

Kyoto 25.pdf

Coffee break

Session

6 Simulating the Euclidean and Lorentzian IKKT model with deformations

Recently the Euclidean IKKT model with deformation preserving 16 supersymmetries has attracted a lot of attention. In particular, the partition function was evaluated exactly by applying the SUSY localization method, and the "time-less holography" was discovered. Moreover, it was found that the original IKKT model is NOT retrieved in the limit of removing the deformation. Here we provide a new understanding of this intriguing property of the deformed model by performing numerical simulations based on explicit calculations of observables that probe the emergent space-time. We also investigate the Lorentzian IKKT model with analogous deformations by numerical simulations, and present some results suggesting the emergence of (3+1)-dimensional expanding space-time.

Speaker: Jun Nishimura

Nishimura-Kyoto251202v9FIN.pdf

Coffee break

Session

7 Towards holography for the IKKT matrix model

A particularly interesting corner of holographic dualities is the correspondence between type II strings on Dp branes geometries and d = p+1 dimensional super Yang-Mills theories with sixteen supercharges. For the extremal case p=-1, this suggests a holographic duality for the IKKT matrix model. Despite intriguing and highly non-trivial results in the IKKT model, this duality has, until recently, received only limited attention. In this talk, I will consider the lowest supermultiplet of gauge invariant operators of the model and identify its states with the lowest Kaluza-Klein fluctuations of Euclidean IIB supergravity on the dual D(-1) instanton background. I will explain how to construct its holographic bulk realisation as a one-dimensional maximal supergravity with local SO(10) invariance, capturing the full non-linear dynamics. By analyzing the bulk Killing spinor equations, I will present various half-supersymmetric solutions that break SO(10), and discuss the corresponding brane interpretations. I will end with a few remarks on future directions.

Speaker: Franz Ciceri

A supergravity dual for IKKT holography.pdf

Lunch

Free discussion

Wednesday, December 3

Session

8 Gauged matrix models: the Canonical and Microcanonical views

I will discuss recent results on matrix models with a focus on the approach to the large N limit. The discussion will include a description of the Hagedorn transition (confining/deconfining transition) and its Hawking-Page dual. It will be argued that in the low temperature regime the canonical and microcanonical descriptions are not equivalent. We will see that negative specific heat can arise naturally in the microcanonical context.

Speaker: Denjoe O'Connor

Coffee break

Session

9 The Bootstrap Method in matrix theories

The bootstrap method offers a powerful framework for solving theoretical models by systematically solving the optimization problem from the constraints imposed by kinematic and dynamic equalities and inequalities. This approach has demonstrated remarkable efficacy in tackling matrix models, especially in the large N limit and in scenarios complicated by sign problems. In this presentation, we explore the application of the bootstrap method across diverse models, with a particular emphasis on its implementation in the BFSS model, highlighting its potential to address longstanding challenges in this context.

Speaker: Zechuan Zheng

Slides_Matrix_New (1) - Zheng Zechuan.pdf

Lunch

Session

10 New Computational Methods for Matrix Models and the holographic principle

The ability to numerically simulates holographic models based on matrix models in their relevant parameter regions is of paramount importance to gain new insights into how the gauge-gravity correspondence is realized away from analytical regimes.
New numerical techniques developed for studying quantum many-body physics are being applied to matrix models. I will describe tensor network methods and quantum algorithms applied to simplified version of the BMN and BFSS models (with and without fermions) and I will show some numerical experiments using trapped-ion quantum computers.
Moreover, I will show how deep learning methods can also be used to study the quantum properties of small matrix models.
If time permits, I will move away from matrix models to show an example of a quantum computation experiment of the SYK model.

Speaker: Enrico Rinaldi

Quantum_Methods_MM_RinaldiE_45m.pdf

Coffee break

Poster session

Thursday, December 4

Session

11 Duality Orbits of DLCQs and Holography

I will discuss BPS limits of M-theory that lead to U-dual webs of decoupled theories, whose fundamental degrees of freedom are described by matrix theories. The BPS limits are organized by five different duality orbits of M-theory in DLCQs. Via a generalization of the TTbar deformation to p-branes, this leads to a classification of holographic constructions in string theory. I will show that non-Lorentzian geometric techniques play an indispensable role in this framework. By examining the fundamental strings in these decoupled theories, I will argue how (non-)Lorentzian supergravity equations of motion arise from the corners associated with different matrix theories.

Speaker: Ziqi Yan

Ziqi.pdf

Coffee break

Session

12 Strings from Feynman Diagrams

Over 50 years ago, 't Hooft observed the similarity between the Feynman diagram expansion of a large N gauge theory and the topological expansion of a string theory. The purpose of this talk is to make this idea precise for a protected subsector of the AdS/CFT correspondence. Concretely, we show how the Feynman diagram expansion of correlation functions in N=4 SYM preserving half the supersymmetry can be explicitly recast as a dual sum over closed strings. Each individual Feynman diagram maps on to one worldsheet configuration. The weight of the diagram translates to the exponential of the Nambu-Goto action of the dual string.

Speaker: Edward Mazenc

Lunch

Session

13 Localization of the BFSS matrix model

We apply localization to the BFSS matrix model with specific boundary conditions in the time direction, which are related to certain scattering amplitudes in 11-dimensional M-theory. For the boundary conditions corresponding to the three-point graviton amplitude, we compute the partition function exactly using localization and show that the result correctly reproduces the expected momentum dependence of the three-point amplitude.

Speaker: Goro Ishiki

Coffee break

Discussion session

Free discussion

Informal lecture: Monte Carlo algorithm

14 Short review on Monte Carlo algorithm

Speaker: Hiromasa Watanabe

slides_Watanabe.pdf

Friday, December 5

Session

15 Standard Model from IIB Matrix Model

Interpreting the matrices in the IIB matrix model as representing momentum space,
the matrices are described by bilocal fields. Consequently, the IIB matrix model
becomes a pregeometric action describing a system that includes gravity. From
this perspective, we discuss the possibility that the Standard Model emerges as
the effective theory at low energies.
This talk is based on joint work with P.-M. Ho, W. Piensuk, and W.-H. Shao.

Speaker: Hikaru Kawai

YITP25_3 - Hikaru KAWAI.pdf

Coffee break

Session

16 K-theoretic matrix theory and D-branes

We study matrix theories constructed from non-BPS D-particle/D-instanton systems in type IIA/B string theory. In addition to the matrices describing the positions of the D-particles or D-instantons, these theories contain a tachyonic matrix, which plays a central role. The main claims of this talk are as follows:
1) Any D-brane configuration can, in principle, be realized within these matrix theories.
2) Such D-brane configurations are classified by K-homology, in a manner consistent with the K-theory classification of D-brane charges.
3) The effective actions of the resulting D-branes can be derived using the boundary-state formalism.
4) As an application, the Atiyah–Singer index theorem can be obtained through physical considerations.
This talk is an invited review of a series of works carried out in collaboration with T. Asakawa and S. Terashima during the period 2001–2003.

Speaker: Shigeki Sugimoto

K-matrix_2025.pdf

Coffee break

Session

17 Matrix and Geometry in D-Brane Physics

I will present a unified D-brane viewpoint on how matrix configurations encode noncommutative and commutative geometries. First, I explain how noncommutative D-branes and fuzzy geometries arise from bound states of infinitely many unstable D0-branes, where tachyon dynamics project to a finite set of effective D0-branes. I will also show that in the same way, we can describe ADHM and Nahm constructions in boundary state language. Finally, I present a map from matrices to smooth geometries, which can be viewed as a matrix regularization of brane worldvolumes. Together, these results relate matrix models, noncommutative geometry, and D-brane physics in a single framework.

Speaker: Seiji Terashima

Closing