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arXiv · 2212.09549

"Zoology" of non-invertible duality defects: the view from class $\mathcal{S}$

Andrea Antinucci·Christian Copetti·Giovanni Galati·Giovanni Rizi
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Abstract

We study generalizations of the non-invertible duality defects present in $\mathcal{N} = 4$ SU(N) SYM by studying theories with larger duality groups. We focus on 4d $\mathcal{N} = 2$ theories of class $\mathcal{S}$ obtained by the dimensional reduction of the 6d $\mathcal{N} = (2, 0)$ theory of $A_{N-1}$ type on a Riemann surface $\Sigma_g$ without punctures. We discuss their non-invertible duality symmetries and provide two ways to compute their fusion algebra: either using discrete topological manipulations or a 5d TQFT description. We also introduce the concept of "rank" of a non-invertible duality symmetry and show how it can be used to (almost) completely fix the fusion algebra with little computational effort.

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Andrea Antinucci, Christian Copetti, Giovanni Galati, Giovanni Rizi. 2022-12-19. "Zoology" of non-invertible duality defects: the view from class $\mathcal{S}$. https://arxiv.org/abs/2212.09549

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