# Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups

@inproceedings{Gukov2021SymmetriesO2, title={Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups}, author={Sergei Gukov and Du Pei and Charles Reid and Ali Shehper}, year={2021} }

We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. One application of our results is a generalization of the equivariant Verlinde formula to the case of general Lie groups. The generalized formula leads to many predictions…

## 3 Citations

On the 6d Origin of Non-invertible Symmetries in 4d

- Mathematics
- 2022

It is well-known that six-dimensional superconformal ﬁeld theories can be exploited to unravel interesting features of lower-dimensional theories obtained via compactiﬁcations. In this short note we…

Anomalies of Generalized Symmetries from Solitonic Defects

- Physics
- 2022

We propose the general idea that ’t Hooft anomalies of generalized global symmetries can be understood in terms of the properties of solitonic defects, which generically are non-topological defects.…

Disconnected 0-Form and 2-Group Symmetries

- Mathematics, Art
- 2022

Quantum field theories can have both continuous and finite 0-form symmetries. We study global symmetry structures that arise when both kinds of 0-form symmetries are present. The global structure…

## References

SHOWING 1-10 OF 38 REFERENCES

Equivariant Verlinde Formula from Fivebranes and Vortices

- Mathematics
- 2015

We study complex Chern–Simons theory on a Seifert manifold M3 by embedding it into string theory. We show that complex Chern–Simons theory on M3 is equivalent to a topologically twisted…

Conformal blocks, fusion rules and the Verlinde formula

- Mathematics
- 1994

The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one…

D-branes and K-theory in 2D topological field theory

- Mathematics
- 2006

This expository paper describes sewing conditions in two-dimensional open/closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We determine…

Topological gauge theories and group cohomology

- Mathematics
- 1990

We show that three dimensional Chern-Simons gauge theories with a compact gauge groupG (not necessarily connected or simply connected) can be classified by the integer cohomology groupH4(BG,Z). In a…

The equivariant Verlinde formula on the moduli of Higgs bundles

- Mathematics
- 2016

We prove an analog of the Verlinde formula on the moduli space of semistable meromorphic G-Higgs bundles over a smooth curve for a reductive group G whose fundamental group is free. The formula…

Bethe/gauge correspondence on curved spaces

- Physics
- 2014

A bstractBethe/gauge correspondence identifies supersymmetric vacua of massive gauge theories invariant under the two dimensional N$$ \mathcal{N} $$ = 2 Poincare supersymmetry with the stationary…

Verlinde Formulas for Nonsimply Connected Groups

- Mathematics
- 2018

In 1999, Fuchs and Schweigert proposed formulas of Verlinde type for moduli spaces of surface group representations in compact nonsimply connected Lie groups. In this paper, we will prove a…

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence

- MathematicsJournal of High Energy Physics
- 2020

By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2 , 0) theory on a three-manifold M 3 . This generalization is…

Equivariant U(N) Verlinde algebra from Bethe/gauge correspondence

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe compute the topological partition function (twisted index) of N$$ \mathcal{N} $$ = 2 U(N) Chern-Simons theory with an adjoint chiral multiplet on Σg × S1. The localization technique shows…