Charging Up the Functional Bootstrap

TL;DR

This paper develops new analytic functional bases for charged conformal field theory correlators, enabling improved bounds on operator product expansion densities and advancing the understanding of charged bootstrap methods.

Contribution

It introduces two novel sets of analytic functionals for charged correlators, connecting to the Polyakov bootstrap and enhancing bounds on the 3d Ising twist defect.

Findings

Established general bounds on OPE density for charged correlators

Developed dual functional basis related to charged Polyakov bootstrap

Obtained improved bounds on 3d Ising twist defect

Abstract

We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The first, which we call "simple", is essentially a direct sum of analytic functionals for the uncharged case. We use it to establish very general bounds on the OPE density appearing in charged correlators. The second basis is dual to generalized free fields and we explain how it is related to a charged version of the Polyakov bootstrap. We apply these functionals to map out the space of correlators and obtain new improved bounds on the 3d Ising twist defect.