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arXiv · 2412.06729

Non-invertible twisted compactification of class $\mathcal S$ theory and $(B,B,B)$ branes

Yankun Ma
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Abstract

We study non-invertible twisted compactification of class $\mathcal S$ theories on $S^1$: we insert a non-invertible symmetry defect at $S^1$ extending along remaining directions and then compactify on $S^1$. We show that the resulting 3d theory is 3d $\mathcal N=4$ sigma model whose target space is a hyperK\"ahler submanifold of Hitchin moduli space, i.e. a $(B,B,B)$ brane. The $(B,B,B)$ brane is the fixed point set on Hitchin moduli space of a finite subgroup of mapping class group of underlying Riemann surface. We describe the $(B,B,B)$ branes as affine varieties and calculate concrete examples of these $(B,B,B)$ branes for type $A_1$, genus $2$ class $\mathcal S$ theory.

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Yankun Ma. 2024-12-09. Non-invertible twisted compactification of class $\mathcal S$ theory and $(B,B,B)$ branes. https://arxiv.org/abs/2412.06729

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