A tale of 2-groups: Dp(USp(2N)) theories

Abstract

A 1-form symmetry and a 0-form symmetry may combine to form an extension known as the 2-group symmetry. We find the presence of the latter in a class of Argyres-Douglas theories, called Dp(USp(2N)), which can be realized by ℤ2-twisted compactification of the 6d $$ \mathcal{N} $$ N = (2, 0) of the D-type on a sphere with an irregular twisted puncture and a regular twisted full puncture. We propose the 3d mirror theories of general Dp(USp(2N)) theories that serve as an important tool to study their flavor symmetry and Higgs branch. Yet another important result is presented: we elucidate a technique, dubbed “bootstrap”, which generates an infinite family of $$ {D}_p^b(G) $$ D p b G theories, where for a given arbitrary group G and a parameter b, each theory in the same family has the same number of mass parameters, same number of marginal deformations, same 1-form symmetry, and same 2-group structure. This technique is utilized to establish the presence or absence of the 2-group symmetries in several classes of $$ {D}_p^b(G) $$ D p b G theories. In this regard, we find that the Dp(USp(2N)) theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.

Comments on Non-invertible Symmetries in Argyres-Douglas Theories

“…In the present work we will be primarily concerned with the SCFTs of D p (G) type [97][98][99] and their gauging. In the context of geometric engineering and class S, it has been discovered that several of such AD theories possess non-trivial 1-form [100][101][102][103] and 2-group symmetries [103,104]. The presence of these symmetries brings about rich dynamical consequences that have been studied in our previous work [104,105].…”