Classification of large N superconformal gauge theories with a dense spectrum

Ki-Hong Lee,Jaewon Song,Prarit Agarwal

doi:10.1007/jhep10(2021)049

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 N2 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.

Highlights

There are several recent attempts to classify superconformal gauge theories in 4d, for example with N = 2 supersymmetry [14], all possible IR fixed points obtained via superpotential deformations [15, 16], and the ones connected to free theory via exactly marginal deformations [17]
We propose that during any single iteration, the correct a-maximization procedure involves removing only that unitarityviolating operator, which has the lowest scaling dimension at that point. This cycle has to be repeated over and over until there are no more operators to decouple. We find another interesting issue that arises from the decoupling of operators: the ‘baryonic flavor symmetry’ in the UV can mix with the R-symmetry in the IR, contrary to the usual expectation
We have restricted the analysis to the cases with fixed flavor symmetry and no superpotential

Summary

Classification of large N supersymmetric gauge theories

Let us discuss our scheme of classification. We will be considering four-dimensional N = 1 supersymmetric gauge theories that flow to interacting superconformal fixed points (without a superpotential) in the infrared with the following assumptions:. In 4d N = 4 SYM theory and the N = 2 superconformal QCD, the chiral operators are given by gauge-invariant combinations of the adjoint and the fundamental chiral multiplets of the form TrΦi and QΦjQ These have an O(1) gap ( exactly 1) in the large N limit. Recall that in our scheme of classification, theories with a dense spectrum include at most a single adjoint chiral multiplet, in which case the r.h.s. of (2.4) becomes vanishingly small. For SO(N ) and Sp(N ) theories, we will include a single rank-2 tensor For these gauge groups, the ratio T (adj)/T (Rrank 2) → 1 in the large-N limit, once again ensuring that the r.h.s. of (2.4) becomes vanishingly small. For the dense theories, a − c is of the same order as a and c, we do not expect a/c to approach 1.6

Renormalization group flow and the ordering of decoupling

Weak Gravity Conjecture in AdS

CT QB 40 CB Δ

One symmetric and Nf fundamentals

One anti-symmetric and Nf fundamentals

Conclusion and discussion