A tale of 2-groups: Dp(USp(2N)) theories
Federico Carta, Simone Giacomelli, Noppadol Mekareeya, Alessandro Mininno
Abstract
A bstract 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(2 N )), which can be realized by ℤ 2 -twisted compactification of the 6d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (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(2 N )) 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 $$ {D}_p^b(G) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>p</mml:mi> <mml:mi>b</mml:mi> </mml:msubsup> <mml:mfenced> <mml:mi>G</mml:mi> </mml:mfenced> </mml:math> 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 $$ {D}_p^b(G) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>p</mml:mi> <mml:mi>b</mml:mi> </mml:msubsup> <mml:mfenced> <mml:mi>G</mml:mi> </mml:mfenced> </mml:math> theories. In this regard, we find that the D p (USp(2 N )) theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.