Name: Categorical Symmetries in Quantum Field Theory (Conference and School)
Start: 2023-08-27T09:00:00+02:00
End: 2023-09-08T12:15:00+02:00
Location: SRS

Monday, August 21, 2023
Tuesday, August 22, 2023
Wednesday, August 23, 2023
Thursday, August 24, 2023
Friday, August 25, 2023
Saturday, August 26, 2023
Sunday, August 27, 2023

Monday, August 28, 2023

9:00 AM Christoph Schweigert: String-net methods for CFT correlators
Christoph Schweigert: String-net methods for CFT correlators
9:00 AM - 10:00 AM
Based on a graphical calculus for pivotal bicategories, we develop a string-net construction of a modular functor. We show that a rigid separable Frobenius functor between strictly pivotal bicategories induces a linear map between the corresponding bicategorical string-net spaces that is compatible with the mapping class group actions and with sewing. This result implies that correlators of two-dimensional conformal field theories factorize over string-net spaces constructed from defect data.

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Anton Kapustin: Symmetries, anomalies, and the bulk-boundary correspondence
Anton Kapustin: Symmetries, anomalies, and the bulk-boundary correspondence
10:15 AM - 11:15 AM
’t Hooft anomalies are obstructions to gauging a global symmetry of a QFT. In one spatial dimension ’t Hooft anomaly of a Lie group symmetry can also be described purely algebraically, without a reference to gauging: it manifests itseld a non-trivial central extension of the current algebra. In higher dimensions, there is no completely satisfactory algebraic reformulation of ’t Hooft anomaly. In this talk, I will argue that such an algebraic reformulation should involve higher-form symmetries. To support this claim I will discuss analogous issues for gapped lattice systems in one dimension higher which are related to QFT via the bulk-boundary correspondence.

11:15 AM Mayuko Yamashita: Topological modular forms and heretoric string theory
Mayuko Yamashita: Topological modular forms and heretoric string theory
11:15 AM - 12:15 PM
In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways.

4:00 PM Coffee break
Coffee break
4:00 PM - 4:45 PM

4:45 PM Simons Dialogue
Simons Dialogue
4:45 PM - 5:45 PM
Tuesday, August 29, 2023

9:00 AM Maissam Barkeshli: TBA
Maissam Barkeshli: TBA
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Mathew Bullimore: Representation theory for categorical symmetries
Mathew Bullimore: Representation theory for categorical symmetries
10:15 AM - 11:15 AM
My talk is about how categorical symmetries act on and organise the spectrum of non-topological extended operators in QFT. I will address this question from two equivalent perspectives: the representation theory of higher tube algebras and the sandwich construction of symmetries via the Drinfeld center. I'll discuss a variety of examples in three dimensions: invertible symmetries and higher twisted Drinfeld doubles, Ising-like symmetries, and braided fusion symmetries. Based on https://arxiv.org/abs/2305.17165.

11:15 AM Chelsea Walton: Reflective centers of module categories and quantum K-matrices
Chelsea Walton: Reflective centers of module categories and quantum K-matrices
11:15 AM - 12:15 PM
This talk will be on recent joint work with Robert Laugwitz and Milen Yakimov (arXiv:2307.14764) that is motivated by obtaining solutions to the quantum reflection equation (qRE). To start, given a braided monoidal category C and C-module category M, we introduce a version of the Drinfeld center Z(C) of C adapted for M. We refer to this category as the "reflective center" E_C(M) of M. Just like Z(C) is a canonical braided monoidal category attached to C, we show that E_C(M) is a canonical braided module category attached to M. When C is the category of modules over a quasitriangular Hopf algebra H, and M is the category of modules over an H-comodule algebra A, we show that E_C(M) is equivalent to a category of modules over an explicit algebra, which we call the "reflective algebra" R_H(A) of A. Here, R_H(A) is akin to Drinfeld double of H. We show that reflective algebras are quasitriangular H-comodule algebras, and examine their corresponding quantum K-matrices (which are solutions to the qRE).

4:00 PM Coffee break
Coffee break
4:00 PM - 4:45 PM

5:45 PM Gong Show
Gong Show
5:45 PM - 6:45 PM
Wednesday, August 30, 2023

9:00 AM Gong Show
Gong Show
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Catherine Meusburger: Turaev-Viro-Barrett-Westbury state sums with defects
Catherine Meusburger: Turaev-Viro-Barrett-Westbury state sums with defects
10:15 AM - 11:15 AM
We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface defects (oriented 2d surfaces), line defects and point defects (graphs on the defect surfaces). Surface defects are labeled with bimodule categories over spherical fusion categories with bimodule traces, line and point defects with bimodule functors and bimodule natural transformations. The state sum uses generalised 6j symbols that encode the coherence isomorphisms of the defect data. We prove the triangulation independence of the state sum and show that it can be computed with polygon diagrams that satisfy the cutting and gluing identities for polygon presentations of oriented surfaces. State sums detect the genus of a defect surface and are sensitive to its embedding. Defect lines on defect surfaces with trivial defect data define ribbon invariants for the centre of the underlying spherical fusion category. Reference: C. Meusburger, State sum models with defects based on spherical fusion categories, Adv. Math. 429 (2023), DOI:10.1016/j.aim.2023.109177

11:15 AM Sakura Schafer-Nameki: Categorical Symmetries and Generalized Charges
Sakura Schafer-Nameki: Categorical Symmetries and Generalized Charges
11:15 AM - 12:15 PM
I will give a summary of recent works on global categorical symmetries in QFTs, with a focus on non-invertible symmetries and their description in terms of fusion higher categories. In addition to discussing the symmetries, I will also introduce the notion of a generalized charge, and provide several examples of this for both invertible and non-invertible symmetries.

4:00 PM Coffee break
Coffee break
4:00 PM - 4:45 PM
Thursday, August 31, 2023

9:00 AM Owen Gwilliam: Symmetries via factorization algebras
Owen Gwilliam: Symmetries via factorization algebras
9:00 AM - 10:00 AM
Factorization algebras arose in topology and representation theory but also provide a framework for describing the observables and symmetries of a field theory. This talk will begin by surveying factorization algebras and what they do well -- and do not -- in physics, at least at present. In the latter part we will describe work in progress with Araminta Amabel on selection rules for line operators of gauge theories, transposing Dan Freed's argument into the key of factorization algebras.

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Kenneth Intriligator: Anomalies of 4d Spin_G theories
Kenneth Intriligator: Anomalies of 4d Spin_G theories
10:15 AM - 11:15 AM
We consider ’t Hooft anomalies for a variety of 4d gauge theories whose fermion matter content admits Spin_G(4) generalized spin structure, with G gauged or global. We discuss and compute the w2 w3 type ’t Hooft anomalies that arise in this context, and aspects of anomaly matching in the possible IR phases. Based on work with T. Daniel Brennan.

11:15 AM Kevin Walker: Categorified idempotent completion, topological symmetries of QFTs, and generalized Kramers-Wannier duality
Kevin Walker: Categorified idempotent completion, topological symmetries of QFTs, and generalized Kramers-Wannier duality
11:15 AM - 12:15 PM
Any (n-pivotal) n-category C can be embedded in a Morita-equivalent completion C^#. Because of the Morita equivalence, any module/action of C automatically leads to one of the larger category C^#. In particular, discrete k-form symmetries of d-dimensional QFTs correspond to actions of C(G, d+1, k+1) = \pi_{\le d+1}(B^{k+1}(G)), and therefore give rise to actions of the completed (d+1)-category C(G, d+1, k+1)^#. While C(G, d+1, k+1) is built out of invertible morphisms, C(G, d+1, k+1)^# typically contains many non-invertible morphisms leading to non-invertible symmetries of the original QFT. I’ll also discuss how completed n-categories can be used to construct many new examples of Kramers-Wannier-type dualities. This is joint work with Fiona Burnell.

4:00 PM Coffee break
Coffee break
4:00 PM - 4:45 PM

5:45 PM Zohar Komargodski: Applications of Symmetries for Conformal Defects
Zohar Komargodski: Applications of Symmetries for Conformal Defects
5:45 PM - 6:45 PM
Friday, September 1, 2023

9:00 AM Kantaro Ohmori: Non-supersymmetric heterotic branes, bordisms, 2d SCFTs
Kantaro Ohmori: Non-supersymmetric heterotic branes, bordisms, 2d SCFTs
9:00 AM - 10:00 AM
The no-bordism conjecture by McNamara and Vafa states that the bordism group with tangential structure and branes (singularity types) for a consistent quantum gravity should vanish. This predicted previously unknown non-supersymmetric branes in string theory which should cancel the apparently nontrivial bordism classes. In this talk I will propose the worldsheet theories of a string in the throat region of some of the predicted new branes in heterotic string theory. I will also describe the relation to Stolz-Teichner conjecture as a connection to Yamashita’s talk. The no-bordism conjecture by McNamara and Vafa states that the bordism group with tangential structure and branes (singularity types), for consistent quantum gravity, should vanish. As a corollary of the conjecture they predicted previously unknown non-supersymmetric branes in string theory, which are required to cancel the apparently nontrivial bordism classes. In this presentation, I will propose the worldsheet theories of a string in the throat region of some of the predicted branes in heterotic string theory. Additionally, I will mention the relationship to the Stolz-Teichner conjecture and connect it to Yamashita’s talk.

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM David Ayala: Derived Skein modules via factorization homology
David Ayala: Derived Skein modules via factorization homology
10:15 AM - 11:15 AM
In this talk, I will motivate derived Skein modules, which recover (classical) Skein modules while possessing a host of expected continuous symmetries, functorialities, and local-to-global formulae. Then, using factorization homology, I will outline how to construct derived Skein modules.
Saturday, September 2, 2023
Sunday, September 3, 2023

Monday, September 4, 2023

9:00 AM Shu-Heng Shao: Non-invertible Symmetries
Shu-Heng Shao: Non-invertible Symmetries
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Shu-Heng Shao: Non-invertible Symmetries
Shu-Heng Shao: Non-invertible Symmetries
10:15 AM - 11:15 AM

11:15 AM David Jordan: Applied Cobordism Hypothesis
David Jordan: Applied Cobordism Hypothesis
11:15 AM - 12:15 PM

3:30 PM David Jordan: Applied Cobordism Hypothesis
David Jordan: Applied Cobordism Hypothesis
3:30 PM - 4:30 PM

4:30 PM Coffee break
Coffee break
4:30 PM - 5:00 PM

5:00 PM Discussion
Discussion
5:00 PM - 6:00 PM
Tuesday, September 5, 2023

9:00 AM Shu-Heng Shao: Non-invertible Symmetries
Shu-Heng Shao: Non-invertible Symmetries
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Shu-Heng Shao: Non-invertible Symmetries
Shu-Heng Shao: Non-invertible Symmetries
10:15 AM - 11:15 AM

11:15 AM Constantin Teleman: The Mathematics of TQFTs and Defects
Constantin Teleman: The Mathematics of TQFTs and Defects
11:15 AM - 12:15 PM

3:30 PM Constantin Teleman: The Mathematics of TQFTs and Defects
Constantin Teleman: The Mathematics of TQFTs and Defects
3:30 PM - 4:30 PM

4:30 PM Coffee break
Coffee break
4:30 PM - 5:00 PM

5:00 PM Shu-Heng Shao: Non-invertible Symmetries
Shu-Heng Shao: Non-invertible Symmetries
5:00 PM - 6:00 PM

6:00 PM Discussion
Discussion
6:00 PM - 7:00 PM

8:00 PM Gong Show
Gong Show
8:00 PM - 10:00 PM
Wednesday, September 6, 2023

9:00 AM Michele Del Zotto: Symmetry Categories 101
Michele Del Zotto: Symmetry Categories 101
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Michele Del Zotto: Symmetry Categories 101
Michele Del Zotto: Symmetry Categories 101
10:15 AM - 11:15 AM

11:15 AM David Jordan: Applied Cobordism Hypothesis
David Jordan: Applied Cobordism Hypothesis
11:15 AM - 12:15 PM

4:30 PM Coffee break
Coffee break
4:30 PM - 5:00 PM

5:00 PM David Jordan: Applied Cobordism Hypothesis
David Jordan: Applied Cobordism Hypothesis
5:00 PM - 6:00 PM

6:00 PM Discussion
Discussion
6:00 PM - 7:00 PM
Thursday, September 7, 2023

9:00 AM Michele Del Zotto: Symmetry Categories 101
Michele Del Zotto: Symmetry Categories 101
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Michele Del Zotto: Symmetry Categories 101
Michele Del Zotto: Symmetry Categories 101
10:15 AM - 11:15 AM

11:15 AM Constantin Teleman: The Mathematics of TQFTs and Defects
Constantin Teleman: The Mathematics of TQFTs and Defects
11:15 AM - 12:15 PM

4:30 PM Coffee break
Coffee break
4:30 PM - 5:00 PM

5:00 PM Constantin Teleman: The Mathematics of TQFTs and Defects
Constantin Teleman: The Mathematics of TQFTs and Defects
5:00 PM - 6:00 PM

6:00 PM Discussion
Discussion
6:00 PM - 7:00 PM
Friday, September 8, 2023

9:00 AM David Jordan: Applied Cobordism Hypothesis
David Jordan: Applied Cobordism Hypothesis
9:00 AM - 10:00 AM

10:00 AM Coffee break
Coffee break
10:00 AM - 10:15 AM

10:15 AM Constantin Teleman: The Mathematics of TQFTs and Defects
Constantin Teleman: The Mathematics of TQFTs and Defects
10:15 AM - 11:15 AM

11:15 AM Michele Del Zotto: Symmetry Categories 101
Michele Del Zotto: Symmetry Categories 101
11:15 AM - 12:15 PM

Choose timezone

Share this page

Direct link

Social networks

Calendaring