4d N $$ \mathcal{N} $$ =2 theories with disconnected gauge groups

Abstract

Abstract In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 N $$ \mathcal{N} $$ = 2 SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 N $$ \mathcal{N} $$ = 2 SCFTs. The global symmetries that can be gauged involve a non-trivial combination of discrete subgroups of the U(1) R , low-energy EM duality group S L 2 , ℤ $$ \mathrm{S}\mathrm{L}\left(2,\kern0.5em \mathbb{Z}\right) $$ , and the outer automorphism group of the flavor symmetry algebra, Out(F ). The theories that we construct are remarkable in many ways: (i) two of them have exceptional F 4 and G 2 flavor groups; (ii) they substantially complete the picture of the landscape of rank-1 N $$ \mathcal{N} $$ = 2 SCFTs as they realize all but one of the remaining consistent rank-1 Seiberg-Witten geometries that we previously constructed but were not associated to known SCFTs; and (iii) some of them have enlarged N $$ \mathcal{N} $$ = 3 SUSY, and have not been previously constructed. They are also examples of SCFTs which violate the ShapereTachikawa relation between the conformal central charges and the scaling dimension of the Coulomb branch vev. We propose a modification of the formulas computing these central charges from the topologically twisted Coulomb branch partition function which correctly compute them for discretely gauged theories.

Keywords

• Conformal Field Theory
• Discrete Symmetries
• Extended Supersymmetry
• Supersymmetry and Duality