Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups
Abstract
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 0form symmetries always act as permutations while 1form 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 for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus and SO(3) gauge group.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.08032
 Bibcode:
 2021arXiv211108032G
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 39 pages, 6 figures