Classification of large N superconformal gauge theories with a dense spectrum

TL;DR

This paper classifies large N superconformal gauge theories in four dimensions, identifying 8 with a dense spectrum of operators, and explores their properties, central charges, and implications for the Weak Gravity Conjecture.

Contribution

It provides a comprehensive classification of large N superconformal gauge theories with dense spectra and analyzes their central charges and spectrum structure, revealing new insights into their properties.

Findings

8 theories with dense spectra identified

Central charges grow linearly with N for dense theories

Dense theories satisfy the Weak Gravity Conjecture at large N

Abstract

We classify the large $N$ limits of four-dimensional supersymmetric gauge theories with simple gauge groups that flow to superconformal fixed points. We restrict ourselves to the ones without a superpotential and with a fixed flavor symmetry. We find 35 classes in total, with 8 having a dense spectrum of chiral gauge-invariant operators. The central charges $a$ and $c$ for the dense theories grow linearly in $N$ in contrast to the $N^2$ growth for the theories with a sparse spectrum. The difference between the central charges $a-c$ can have both signs, and it does not vanish in the large $N$ limit for the dense theories. We find that there can be multiple bands separated by a gap, or a discrete spectrum above the band. We also find a criterion on the matter content for the fixed point theory to possess either a dense or sparse spectrum. We discover a few curious aspects regarding supersymmetric RG flows and $a$-maximization along the way. For all the theories with the dense spectrum, the AdS version of the Weak Gravity Conjecture (including the convex hull condition for the cases with multiple $U(1)$'s) holds for large enough $N$ even though they do not have weakly-coupled gravity duals.