# Main Page

**Global Categorical Symmetries Seminars**[edit]

Welcome to the wiki for the seminar on **Global Categorical Symmetries**.

We will use this wiki to collect information, references, and links to interesting videos to watch.

**Seminars**[edit]

Our seminars are held fortnightly on

**Friday at 9.30 Pacific, 12.30 Eastern, 18.30 European time**

in this digital room.

The recordings of the seminars are available **here**

### 20201009. Clay Córdova: *Symmetry Enforced Gaplessness*[edit]

Clay will discuss some aspects of his works with Kantaro where they derived some restrictions on anomalies of TQFTs

There are also nice converse results recently proven by Ryan

### 20201023. Dan Freed: *Anomalies and invertible field theories in two acts, with prologue and epilogue*[edit]

A few pertinent expositions are:

- https://arxiv.org/abs/1905.09315 (esp. section 1)

Slides from the talk are available at https://web.ma.utexas.edu/users/dafr/sccs

### 20201106. Theo Johnson-Freyd: *Some examples in fusion 2-categories and 3+1D topological order*[edit]

**Abstract:** I have spent the last couple months computing everything I can about the (extended) operator content of a trio of closely related 3+1D bosonic topological orders (≈TFTs): ℤ2 gauge theory, spin-ℤ2 gauge theory, and an anomalous version of spin-ℤ2 gauge theory. [Nontrivial theorem: these are precisely the three 3+1D topological orders with a unique nontrivial particle.] I will tell you some of the results of my computations. In other words, I will tell you the "global categorical symmetries" of these three topological orders. My hope is to illustrate some phenomena that can occur in fusion 2-categories.

Some preliminary readings:

Slides from this talk: http://categorified.net/SCCSslides.pdf

### 20201120. Thomas T. Dumitrescu: *Some Examples and Applications of Continuous 2-Group Symmetries*[edit]

Based on:

### 20201204. Alberto Cattaneo: *BV-BFV and Quantization on Manifolds with Corner*[edit]

Based on:

- A. S. Cattaneo, P. Mnev, N. Reshetikhin, Classical BV Theories on Manifolds with Boundary, Commun. Math. Phys. 332, 535-603 (2014)
- A. S. Cattaneo, P. Mnev, N. Reshetikhin, Classical and Quantum Lagrangian Field Theories with Boundary, PoS(CORFU2011)044
- A. S. Cattaneo, P. Mnev, N. Reshetikhin, Perturbative quantum gauge theories on manifolds with boundary, Commun. Math. Phys. 357, 631–730 (2018), https://arxiv.org/abs/1507.01221
- A. S. Cattaneo, N. Moshayedi, Introduction to the BV-BFV formalism, Reviews in Mathematical Physics Vol. 32(2020) 2030006, https://arxiv.org/abs/1905.08047

** First Workshop **[edit]

On Friday 18, Monday 21 and Wednesday 23 of December.

First talk starts at: 8 AM Pacific, 11 Eastern, 5 PM European. Each talks lasts for 45 minutes + 15 minutes for questions + 15 minutes break.

Please feel free to bring your breakfast/lunch/dinner along!

**FRIDAY 18**

### Iñaki García Etxebarria: *Flux non-commutativity and higher form symmetries of field theories*[edit]

I review how the results of Freed, Moore and Segal on non-commutativity of fluxes in the presence of torsion can be used to rederive a number a results in the literature regarding the possible global form of quantum field theories (for instance, the choice between SU(2) and SO(3)_+ and SO(3)_- for an N=4 theory with gauge algebra su(2), or the structure of conformal blocks for the (2,0) theories in 6d). This approach does not require knowledge of a Lagrangian, and it extends easily to many classes of theories for which we have a geometric construction in string theory, but no known gauge theory description.

Based on https://arxiv.org/abs/1908.08027, https://arxiv.org/abs/2005.12831 and https://arxiv.org/abs/2007.15603.

### Ryan Thorngren: *Classifying spaces, bundles of theories, and some applications*[edit]

There is a correspondence between representations of a group G and vector bundles on its classifying space BG. This is akin to gauging, where we replace a theory with a G action by a theory coupled to a background gauge field, in other words a map to BG. This leads us to consider a notion of bundles of theories over BG, and indeed over any space. I will describe some applications of this point of view, including how anomalies can be thought of as projective bundles, how the bundle picture leads to a classification of crystalline topological phases, and how it inspires us to study notions of higher Berry phase.

References:

``Spaces as infinity-groupoids" T. Porter https://ncatlab.org/nlab/files/Spaces+as+infinity-groupoids.pdf

``Fusion categories and homotopy theory" P. Etingof, D. Nikshych, V. Ostrik https://arxiv.org/abs/0909.3140

``Gauging spatial symmetries and the classification of crystalline topological phases" R. Thorngren, D. Else https://arxiv.org/abs/1612.00846

``Berry phase in quantum field theory: diabolical points and boundary phenomena" P-S. Hsin, A. Kapustin, R. Thorngren https://arxiv.org/abs/2004.10758

Slides:

File:Classifying-spaces-bundles-of-theories-and-some-applications.pdf

### Ibou Bah: *Anomaly inflow and topological mass terms*[edit]

**MONDAY 21**

### David Jordan[edit]

### Michele Del Zotto: *Some preliminaries about global symmetries and categories of branes*[edit]

### Constantin Teleman: *Towards a Universal Target for TQFTs*[edit]

**WEDNESDAY 23**

### Mathew Bullimore: *Defects and Co-isotropic Structures*[edit]

### Julia Plavnik: *Gauging and Zesting Modular Tensor Categories*[edit]

### Kantaro Ohmori: *Categorical Symmetry in 1+1 Adjoint QCD*[edit]

**References**[edit]

The recordings of the seminars are available **here**

to videos

to bibliography

Please help by adding more videos and references you think might be interesting.