On Arnold's 14 `exceptional' N=2 superconformal gauge theories

TL;DR

This paper explores four-dimensional N=2 superconformal gauge theories linked to Arnold's 14 exceptional singularities, computing their BPS spectra and constructing new Y-systems, thereby extending the understanding of these theories beyond minimal cases.

Contribution

It extends previous methods to non-minimal singularities, computes BPS spectra in strongly coupled chambers, and constructs new periodic Y-systems for these complex theories.

Findings

Computed BPS spectra for theories associated with Arnold's singularities.

Constructed ten new periodic Y-systems supporting conjectures about their universality.

Provided evidence for the existence of periodic Y-systems for all isolated quasi-homogeneous singularities with <2.

Abstract

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to singularities which are not the direct sum of minimal ones. In particular, we compute their BPS spectra in several `strongly coupled' chambers. From the TBA side, we construct ten new periodic Y-systems, providing additional evidence for the existence of a periodic Y-system for each isolated quasi-homogeneous singularity with $\hat c<2$ (more generally, for each N=2 superconformal theory with a finite BPS chamber whose chiral primaries have dimensions of the form N/l).