Large N gauge theories with a dense spectrum and the weak gravity conjecture

Prarit Agarwal,Jaewon Song

doi:10.1007/jhep05(2021)124

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 mathcal{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(N1) contrary to the usual O(N2) 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.

Highlights

In this paper, we show that there exists large N gauge theories with dense spectrum at low-energy
We find the AdS version of the Weak Gravity Conjecture (WGC) holds for this theory, it cannot be holographically dual to supergravity
We showed that there exist large N gauge theories with the dense low-lying spectrum, and the degrees of freedom measured by the central charges grow linearly in N

Summary

The model

An additional caveat arises from the fact that all the operators must satisfy the unitarity constraint: any gauge-invariant chiral operators should have a scaling dimension ∆. During the course of a-maximization, it often happens that the resulting value of R-charges causes certain chiral operator dimensions to drop to 1 or lower. This indicates that the corresponding operator gets decoupled along the renormalization group flow. Its contribution to the a-function must be removed, following which a-maximization has to be redone [12]. This cycle needs to be iterated over until no more operators decouple. The role of the flip field has been investigated further in [14,15,16], for example

A band of dense spectrum

Testing the weak gravity conjecture

Another model

Discussion