Global Categorical Symmetries Seminars
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.
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
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
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
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
20201204. Alberto Cattaneo: BV-BFV and Quantization on Manifolds with Corner
- 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 
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!
Iñaki García Etxebarria: Flux non-commutativity and higher form symmetries of field theories
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.
Ryan Thorngren: Classifying spaces, bundles of theories, and some applications
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.
``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
Ibou Bah: Anomaly inflow and topological mass terms
Michele Del Zotto: Some preliminaries about global symmetries and categories of branes
Constantin Teleman: Towards a Universal Target for TQFTs
Mathew Bullimore: Defects and Co-isotropic Structures
Julia Plavnik: Gauging and Zesting Modular Tensor Categories
Kantaro Ohmori: Categorical Symmetry in 1+1 Adjoint QCD
The recordings of the seminars are available here
Please help by adding more videos and references you think might be interesting.