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 for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus and SOp3q gauge group.
We study theories of type D 4 in class-S, with nonabelian outer-automorphism twists around various cycles of the punctured Riemann surface C. We propose an extension of previous formulae for the superconformal index to cover this case and classify the SCFTs corresponding to fixtures (3-punctured spheres). We then go on to study families of SCFTs corresponding to once-punctured tori and 4-punctured spheres. These exhibit new behaviours, not seen in previous investigations. In particular, the generic theory with 4 punctures on the sphere from non-commuting Z 2 twisted sectors has six distinct weakly-coupled descriptions.
Given a 4d $$ \mathcal{N} $$
N
= 2 superconformal theory with an $$ \mathcal{N} $$
N
= (2, 2) superconformal surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE.
Given a 4d N = 2 supersymmetric theory with an N = (2, 2) supersymmetric surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE.
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