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Topics in Representation Theory
Non-invertible twisted compactification of class S theory and (B,B,B) branes
Non-invertible twisted compactification of class S theory and (B,B,B) branes
Organizer
Speaker
Yankun Ma
Time
Monday, January 20, 2025 1:00 PM - 2:30 PM
Venue
A14-201
Online
Zoom 242 742 6089
(BIMSA)
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. This talk is based on 2412.06729.