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

Abstract

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 ℤ2-twisted compactification of the 6d N $$ \mathcal{N} $$ = (2, 0) of the D-type on a sphere with an irregular twisted puncture and a regular twisted full puncture. We propose the 3d 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 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 D p (USp(2N)) theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.

Keywords

• Extended Supersymmetry
• Global Symmetries
• Supersymmetric Gauge Theory