Physics and Mathematics of Generalized Symmetry in QFT

24 Aug 2026, 09:00 → 28 Aug 2026, 15:30 Asia/Tokyo

Lecture Hall (Kavli IPMU)

Overview

Generalized symmetries extend ordinary global symmetries by encoding symmetry operations as topological operators, including higher-form and non-invertible examples naturally organized by higher fusion categories. They have reshaped questions in QFT and related areas, from anomalies, gauging, symmetry breaking, and RG flows to string compactifications, CFTs, lattice systems, and topological phases.

The subject also has a rich mathematical side, connected to higher categories, fusion and braided tensor categories, topology, homotopy theory, and higher algebra. This conference brings physicists and mathematicians together to clarify the dictionary between these languages and discuss recent progress at the interface of generalized symmetry, quantum field theory, and mathematics.

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Invited Speakers: 

• Yichul Choi (IAS Princeton)

• Mirjam Cvetič (University of Pennsylvania)

• Markus Dierigl (CERN)

• Iñaki García-Etxebarria (Durham University)

• Justin Kaidi (Kyushu University)

• Sungjay Lee (KIAS)

• Ruben Minasian (IPhT Saclay)

• Yu Nakayama (YITP, University of Kyoto)

• Kantaro Ohmori (RIKEN)

• Du Pei (University of Southern Denmark)

• Pavel Putrov (ICTP, Trieste)

• Rajath Radhakrishnan (University of Oxford)

• Kazuya Yonekura (Tohoku University)

• Mayuko Yamashita (Perimeter Institute)

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Organizers:

• Saghar S. Hosseini (Kavli IPMU)

• Yuji Tachikawa (Kavli IPMU)

• Masahito Yamazaki (Kavli IPMU & School of Science, University of Tokyo)

• Hao Y. Zhang (Kavli IPMU)

• Yi Zhang (Kavli IPMU) 

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Related Workshop:

The related workshop RIKEN-IPMU mini-workshop on QCA and K-theory will take place at Kavli IPMU on August 24-26, 2026, 15:30-17:00 each day. It is scheduled in different time slots from this conference, so the two do not conflict. Participants are encouraged to attend both.

Monday 24 August

09:00 Safety briefing at Kavli IPMU, Prof. Saeko Hayashi

1 RG flow, Non-invertible symmetries and Matrix Factorization

Speaker: Yu Nakayama

10:10 Tea break

2 Multipartite Entanglement in Fusion-Categorical Lattice Models

The symmetry structure of an $(n+1)$-dimensional quantum field theory is expected to be encoded by a fusion $n$-category. The associated SymTFT, is an $(n+2)$-dimensional topological quantum field theory admitting a natural lattice realization constructed from this categorical data. In this talk, I will discuss what information about the SymTFT can be extracted from multipartite entanglement invariants of the ground state of the lattice model on Euclidean space. I will focus on several particularly tractable cases.

Speaker: Pavel Putrov

11:30 Group Photo

11:50 Lunch break

3 Symmetry TFTs for Continuous Spacetime Symmetries

I will discuss our recent proposal for the Symmetry Topological Field Theory (SymTFT) for global, continuous spacetime symmetries (https://arxiv.org/abs/2509.07965). For a $d$-dimensional theory, it is given by a $(d+1)$-dimensional $BF$-theory for the spacetime symmetry group, and whenever $d$ is even, it includes also Chern-Simons couplings, that encode conformal and gravitational anomalies. This proposal is supported by the similarity to two-dimensional Jackiw-Teitelboim gravity in the $d = 1$ case and the topological limit of four-dimensional gravity in the $d = 3$ case. I will discuss how topological defects constructed from this SymTFT act by applying the associated spacetime symmetry transformation. Finally, I will discuss the relation to gravity and holography.

Speaker: Iñaki García-Etxebarria

15:00 Tea break

4 QCA and K-theory lecture

Speaker: Bowen Yang

Tuesday 25 August

5 Extension of sigma models and anomalies

Sigma models have interesting generalization which corresponds to group extension in gauge theories. In my talk, I first explain topological structure of sigma models related to sigma model anomalies, and then discuss the extension of sigma models and anomalies when they are coupled to matter fields.

Speaker: Kazuya Yonekura

10:00 Tea break

6 Elliptic Coulomb branches

I will report the ongoing work with Samuel DeHority, Wenjun Liu and Mykola Semenyakin on the construction of elliptic Coulomb branches. This is an elliptic cohomology version of the existing ordinary/K-theoretic Coulomb branches via the BFN construction. Thanks to the recent development of the theory of elliptic cohomology, we can carry out the construction in genuine equivariant elliptic cohomology (Topological Modular Forms).

Speaker: Mayuko Yamashita

11:30 Lunch break

7 Resurgence of the Thermal Transition between Bounce and Sphaleron

We study the thermal transition between the bounce and the sphaleron in quantum mechanics with a metastable vacuum from the viewpoint of Borel resurgence. For two models representing a second-order and a first-order transition, we compute the perturbative expansion of the thermal free energy to high orders and extract the leading Borel singularity data $(A,b,S)$ as functions of temperature. The Borel singularity location $A$ reproduces the on-shell action of the dominantsaddle on both sides of the transition, joining smoothly in the second-order case and developing a kink in the first-order case. The characteristic exponent $b$ jumps between $0$ and $1/2$ across the transition, counting the zero modes of the corresponding saddle. The Stokes constant $S$ matches the one-loop determinant around the saddle. The perturbative expansion around the false vacuum thus determines the transition temperature, the order of the transition, and the decay rate including the one-loop prefactor without relying on semiclassical inputs.

Speaker: Sungjay Lee

15:00 Tea break

8 QCA and K-theory lecture

Speaker: Bowen Yang

Wednesday 26 August

9 Breaking Generalized Symmetries in Quantum Gravity

In this talk I will summarize recent advances in the description of symmetry-breaking defects in quantum gravity theories. These are important to ensure that there are no global symmetries in the UV. In particular, I will analyze global symmetries that originate from topological features of the theory at low-energy and can be associated to deformation classes described by bordism groups. I will then use this approach to analyze well-known models such as maximal supergravity theories.

Speaker: Markus Dierigl

10:00 Tea break

10 Unoriented

M-theory partition function is well defined on unorientable manifolds. I will discuss some im/applications of this.

Speaker: Ruben Minasian

11:30 Lunch break

11 Symmetry Theories, Anomalies and η-Invariants (Geometric Engineering and Quiver Approaches)

We present progress on calculation of anomaly coefficients for higher symmetries in quantum field theories (QFTs) both from the perspective of geometric engineering and quiver approaches. Within geometric engineering this data is governed by $\eta$-invariants extracted from the boundary geometry on non-compact Calabi-Yau space $X$. Quiver approach provides a complementary way to extract this data from the path algebra of branes probing $X$. We present explicit results for one-form anomaly coefficients in five-dimensional supersymmetric QFTs, engineered in M-theory on classes non-compact Calabi-Yau three-folds $X$. The quiver approach applies also in situations where the counterpart geometric computation is either combinatorially unwieldy or unknown, such as cones over Einstein-Sasaki spaces.

Speaker: Mirjam Cvetič

15:00 Tea break

12 QCA and K-theory lecture

Speaker: Bowen Yang

Thursday 27 August

13 Symmetry-intertwining Topological lines and boundaries in 1+1d fermions

I will talk about topological lines and boundaries in $(1+1)d$ fermions that intertwines symmetry charges. Based on a joint work with Yunqin Zheng, Masataka Watanabe, Pengcheng Wei.

Speaker: Kantaro Ohmori

10:00 Tea break

14 Flat-gauging lines and boundaries

We discuss aspects of “flat-gauging” in $(1+1)d$ conformal field theories (CFTs). We show how to explicitly compute the dual global symmetries as well as various conformal boundary states of the gauged theory. As an application, we present a full classification of generalized global symmetries of a massless, non-compact free scalar field. We also classify all the conformal boundary states of the free scalar field, as well as all the symmetries and conformal boundaries of the Runkel-Watts CFT, which are closely related to those of the Liouville CFT. Our classifications reproduce all the known symmetries and boundaries of these theories, and we also discover some new ones.

Based on a work in collaboration with Ho Tat Lam, Brandon C. Rayhaun.

Speaker: Yichul Choi

11:30 Lunch break

14:00 Free discussion

15:00 Tea break

15:30 Free discussion

Friday 28 August

15 Dimensional reduction of topological operators

While a generic quantum field theory may admit infinitely many topological operators, their topological nature imposes strong consistency conditions on their structure. In this talk, I will introduce the notion of dimensional reduction of topological operators and discuss some constraints it imposes in various spacetime dimensions. I will explain how these constraints severely restrict the possible non-invertible symmetries of QFTs in spacetime dimensions greater than two. This talk is based on arXiv: 2603.03438.

Speaker: Rajath Radhakrishnan

10:00 Tea break

16 On the classification of 2d TQFTs with time-reversal symmetry

We provide a complete classification of a class of two-dimensional topological quantum field theories with time-reversal symmetry. One of the key ingredients is a generalized Frobenius-Schur indicator, which we also define for line operators in $3d$ TQFTs. We will discuss several applications of the classification to the study of topological phases.

Speaker: Du Pei

11:30 Lunch break

17 Generalized Hecke Relations.

Speaker: Justin Kaidi

15:00 Tea break