Comments on Non-invertible Symmetries in Argyres-Douglas Theories

Abstract

Abstract We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of Dp(SU(N)) theories. The same set of theories that we study can also be realized from 6d $$ \mathcal{N} $$ N = (1, 0) compactification on a torus. The main example in this class is the (A2, D4) theory. We show in detail that this specific theory bears the same structures of non-invertible duality and triality defects as those of $$ \mathcal{N} $$ N = 4 super Yang-Mills with gauge algebra 𝔰𝔲(2). We extend this result to infinitely many other Argyres-Douglas theories in the same family, including those with central charges a = c whose conformal manifold is one dimensional, and those with a ≠ c whose conformal manifold has dimension larger than one. Our result is supported by examining certain special cases that can be realized in terms of theories of class 𝒮.