Alonso Perez-Lona, Daniel Robbins, Eric Sharpe, Thomas Vandermeulen, Xingyang Yu
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Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases
In this paper we discuss gauging noninvertible zero-form symmetries in two
dimensions, extending our previous work. Specifically, in this work we discuss
more general gauged noninvertible symmetries in which the noninvertible
symmetry is not multiplicity free, and discuss the case of Rep$(A_4)$ in
detail. We realize Rep$(A_4)$ gaugings for the $c = 1$ CFT at the exceptional
point in the moduli space and find new self-duality under gauging a certain
non-group algebra object, leading to a larger noninvertible symmetry Rep$(SL(2,
Z_3))$. We also discuss more general examples of decomposition in
two-dimensional gauge theories with trivially-acting gauged noninvertible
symmetries.
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