OPE coefficients in Argyres-Douglas theories

TL;DR

This paper computes and bounds OPE coefficients in Argyres-Douglas theories using localization and bootstrap methods, finding good agreement and providing new insights into operator dimensions in these strongly coupled superconformal theories.

Contribution

It introduces dual approaches—localization and bootstrap—to determine OPE coefficients in Argyres-Douglas theories, a class lacking Lagrangian descriptions, and compares their results.

Findings

Good agreement between localization and bootstrap results for rank-one and rank-two theories.

Derived bounds on the dimensions of lightest neutral unprotected operators.

Provided new quantitative data on OPE coefficients in strongly coupled SCFTs.

Abstract

The calculation of physical quantities in certain quantum field theories such as those of the Argyres-Douglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the four-sphere to compute two-correlators and OPE coefficients in Argyres-Douglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rank-one cases and for the rank-two Argyres-Douglas theories (A_1,A_4) and (A_1,A_5), in the moduli space of pure SU(5) and SU(6) super Yang-Mills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.