Large N Gauge Theories with a Dense Spectrum and the Weak Gravity Conjecture

TL;DR

This paper constructs large N gauge theories with a dense low-energy spectrum, demonstrating the Weak Gravity Conjecture's validity beyond traditional holographic duals, thus supporting its broader applicability in quantum gravity.

Contribution

It introduces a new class of large N gauge theories with a dense spectrum and verifies the Weak Gravity Conjecture in these non-holographic models.

Findings

Spectrum gap scales as 1/N

Central charges scale as O(N)

WGC holds in non-holographic theories

Abstract

We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional N=1 supersymmetric SU(N) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge singlets. The gap in the low-lying spectrum scales as 1/N and the central charges scale as $O(N^1)$ contrary to the usual $O(N^2)$ scaling of ordinary gauge theory coming from the matrix degree of freedom. We find the AdS version of the Weak Gravity Conjecture (WGC) holds for this theory, although it cannot be holographically dual to supergravity. This supports the validity of WGC in a more general theory of quantum gravity.