A tale of 2-groups: D$_p$(USp(2N)) theories

TL;DR

This paper investigates 2-group symmetries in a class of Argyres-Douglas theories called D_p(USp(2N)), proposing new mirror theories and a bootstrap technique to analyze their flavor symmetries and Higgs branches.

Contribution

It introduces a bootstrap method to generate infinite families of theories with shared properties and identifies 2-group symmetries in D_p(USp(2N)) theories, advancing understanding of their structure.

Findings

D_p(USp(2N)) theories possess 2-group symmetries.

The bootstrap technique generates infinite theory families with identical symmetry properties.

Proposed 3d mirror theories facilitate the study of flavor symmetry and Higgs branches.

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 $D_p($USp$(2N))$, which can be realized by $\mathbb{Z}_2$-twisted compactification of the 6d $\mathcal{N}=(2,0)$ of the $D$-type on a sphere with an irregular twisted puncture and a regular twisted full puncture. We propose the $3$d mirror theories of general $D_p($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 $D^b_p(G)$ 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 $D^b_p(G)$ theories. In this regard, we find that the $D_p($USp$(2N))$ theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.