The Bootstrap of Points and Lines

TL;DR

This paper develops a conformal bootstrap approach for boundary 2D CFTs, deriving a positive semi-definite program that yields new bounds on boundary entropy and operator gaps, exemplified on free boson and $ ext{SU}(2)_2$ models.

Contribution

It introduces a novel bootstrap method using multiple correlators to access boundary data and improve bounds on boundary entropy and operator gaps in boundary CFTs.

Findings

Successfully applied to free boson CFT for validation.

Produced new bounds on boundary entropy and operator gaps for $c=3/2$ models.

Enhanced understanding of boundary operator spectra in specific WZW models.

Abstract

We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point function of identical operators in the presence of a boundary, and the four-point function of the same operators on the infinite plane. The mixed-correlator system allows the numerical bootstrap to access new data, like the bulk-to-boundary Operator Product Expansion coefficients, and to strengthen the bounds on observables already contained in the partition function on the annulus, such as the boundary entropy. We test the method on the free boson CFT; then, as a first application, we produce new non-perturbative bounds on the entropy and the gaps in boundary CFTs with central charge $c=3/2,$ with special emphasis on the $\mathfrak{su}(2)_2$ WZW model.