A tale of 2-groups: D$_p$(USp(2N)) theories
Federico Carta, Simone Giacomelli, Noppadol Mekareeya, Alessandro Mininno
TL;DR
The work analyzes 2-group symmetry, a nontrivial extension of 1-form and 0-form symmetries, in a broad family of Argyres-Douglas theories, focusing on $D_p({\rm USp}(2N))$ realized via twisted compactifications of the 6d ${\cal N}=(2,0)$ theory. It introduces a bootstrap construction producing infinite families ${D^{b}_{p}}(G)$ that preserve key invariants (mass parameters, marginal deformations, 1-form symmetry, 2-group structure), and uses this to classify the presence or absence of 2-group symmetry across these theories. A central result is that the $D_p({\rm USp}(2N))$ theories constitute a special class possessing a nontrivial 2-group structure in certain polarizations, with detailed analysis facilitated by proposed 3d mirror theories and explicit examination of zero-, one-, and multi-mass parameter regimes. The work also provides explicit 3d mirrors for these theories, describes how Higgs and Coulomb branches map under the mirrors, and clarifies how puncture closures affect the symmetry structure, thereby advancing understanding of higher-group symmetries in 4d ${\cal N}=2$ SCFTs and the role of bootstrap in organizing these data.
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.