Probing Line Defect CFT with Mixed-Correlator Bootstrability

TL;DR

This paper advances the conformal bootstrap approach for defect CFTs in N=4 Super-Yang-Mills by integrating exact integrability data and analyzing mixed correlators, providing bounds on OPE coefficients across couplings.

Contribution

It extends Bootstrability to charged sectors with mixed correlators, combining integrability, localization, and numerical bootstrap for detailed spectral bounds.

Findings

Computed bounds for 12 OPE coefficients at various couplings

Achieved sharp bounds for lowest states, wider for excited states

Highlighted the importance of non-protected states and further integrability input

Abstract

We continue our study of the defect CFT on a Maldacena-Wilson line in N=4 Super-Yang-Mills theory using Bootstrability -- the conformal bootstrap supplemented with exact integrability data. In this paper, we extend this program to charged sectors of the theory, considering a mixed-correlator setup first introduced by Liendo, Meneghelli, and Mitev. The exact spectrum in all channels is given by integrability at any coupling. Additionally, we use exact expressions for some structure constants fixed by localisation and leverage the exact discrete symmetries of the theory. We analyse the remaining data with the numerical bootstrap, developing an algorithm optimised to scan over a large multidimensional space of OPE coefficients and carve the allowed region with the "cutting surface" procedure. We compute upper and lower bounds for 12 OPE coefficients for several values of the coupling. Our results are sharp for the lowest states in each sector but become quite wide for the excited states due to their near degeneracy. This highlights the need for studying the system with non-protected external states and for further input from integrability in the form of integrated correlators of non-protected operators.