Bounds on SCFTs from Conformal Perturbation Theory

TL;DR

This paper uses conformal perturbation theory to derive bounds on operator dimensions in 4d superconformal field theories, revealing that certain OPEs always contain operators below a specific dimension threshold.

Contribution

It establishes general bounds on operator dimensions in 4d SCFTs using conformal perturbation theory, applicable to Banks-Zaks fixed points and similar theories.

Findings

OPE of a chiral operator with its conjugate contains an operator of dimension less than twice its own.

Bounds are demonstrated for Banks-Zaks fixed points and their generalizations.

The results provide constraints on operator spectra in nearly-free coupled SCFTs.

Abstract

The operator product expansion (OPE) in 4d (super)conformal field theory is of broad interest, for both formal and phenomenological applications. In this paper, we use conformal perturbation theory to study the OPE of nearly-free fields coupled to SCFTs. Under fairly general assumptions, we show that the OPE of a chiral operator of dimension $\Delta = 1+\epsilon$ with its complex conjugate always contains an operator of dimension less than $2 \Delta$. Our bounds apply to Banks-Zaks fixed points and their generalizations, as we illustrate using several examples.