Comments on Non-invertible Symmetries in Argyres-Douglas Theories

TL;DR

This paper uncovers non-invertible symmetries in a broad class of Argyres-Douglas theories, revealing new duality structures and extending known phenomena from $ ext{SU}(2)$ super Yang-Mills to these complex superconformal models.

Contribution

It demonstrates the existence of non-invertible symmetries in infinite families of Argyres-Douglas theories, connecting them to known duality defects and extending the understanding of symmetry structures in these theories.

Findings

Non-invertible symmetries found in Argyres-Douglas theories.

The $(A_2, D_4)$ theory exhibits duality and triality defects similar to $ ext{SU}(2)$ super Yang-Mills.

Results supported by class $ ext{S}$ theory realizations.

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 $D_p(\mathrm{SU}(N))$ theories. The same set of theories that we study can also be realized from 6d $\mathcal{N}=(1,0)$ compactification on a torus. The main example in this class is the $(A_2, D_4)$ theory. We show in detail that this specific theory bears the same structures of non-invertible duality and triality defects as those of $\mathcal{N}=4$ super Yang-Mills with gauge algebra $\mathfrak{su}(2)$. 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 $a\neq c$ 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 $\mathcal{S}$.