Infinitely many N=2 SCFT with ADE flavor symmetry

TL;DR

This paper constructs an infinite series of four-dimensional N=2 superconformal field theories with ADE flavor symmetry, revealing new models and their properties through geometric engineering and categorical analysis.

Contribution

It introduces an infinite family of N=2 SCFTs labeled D(G,s) with ADE flavor symmetry, expanding the landscape of known superconformal theories and their geometric and categorical descriptions.

Findings

D(G,s) models have flavor symmetry G and form an infinite tower.

For G=SU(2), D(SU(2),s) matches known Argyres-Douglas models.

Gauging D(G,s) affects the Yang-Mills beta-function with specific contributions.

Abstract

We present evidence that for each ADE Lie group G there is an infinite tower of 4D N=2 SCFTs, which we label as D(G,s) (with s a positive integer), having (at least) flavor symmetry G. For G=SU(2), D(SU(2),s) coincides with the Argyres--Douglas model of type D_{s+1}, while for larger flavor groups the models are new (but for a few previously known examples). When its flavor symmetry G is gauged, D(G,s) contributes to the Yang-Mills beta-function as s/[2(s+1)] adjoint hypermultiplets. The argument is based on a combination of Type IIB geometric engineering and the categorical deconstruction of arXiv:1203.6743. One first engineers a class of N=2 models which, trough the analysis of their category of quiver representations, are identified as asymptotically-free gauge theories with gauge group G coupled to some conformal matter system. Taking the limit g->0 one isolates the matter SCFT which is our D(G,s).