Bootstrapping ${\mathcal N}=2$ chiral correlators

TL;DR

This paper uses the numerical bootstrap approach to analyze four-dimensional ${ m extbf{N}=2}$ superconformal field theories, focusing on chiral correlators, including mixed correlators, to constrain their operator relations and geometric properties.

Contribution

It extends the bootstrap method to mixed correlators in ${ m extbf{N}=2}$ SCFTs, providing new bounds on chiral ring relations and the Zamolodchikov metric curvature.

Findings

Constraints on Coulomb branch chiral ring relations

Bounds on the curvature of the Zamolodchikov metric

Insights into the structure of ${ m extbf{N}=2}$ SCFTs

Abstract

We apply the numerical bootstrap program to chiral operators in four-dimensional ${\mathcal N}=2$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of ${\mathcal N}=2$ SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.