Bootstrapping Coulomb and Higgs branch operators

TL;DR

This paper uses the numerical conformal bootstrap to analyze correlators of Coulomb and Higgs branch operators in 4d $ N=2$ superconformal theories, providing improved bounds on OPE coefficients and insights into the spectra of Argyres-Douglas models.

Contribution

It introduces enhanced bootstrap bounds for Coulomb and Higgs branch correlators, including mixed correlators with flavor symmetry, advancing the numerical study of Argyres-Douglas theories.

Findings

Improved bounds on OPE coefficients for Argyres-Douglas models

Agreement between bootstrap bounds and large $r$ charge limits

Constraints on conformal data in theories with flavor symmetry

Abstract

We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in $4d$ $\mathcal{N}=2$ superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large $r$ charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.