The discontinuity method in a BCFT

TL;DR

This paper introduces a bootstrap method for boundary conformal field theories using the analytical structure of conformal blocks, applied to an O(N) model to compute correlators and OPE coefficients near four dimensions.

Contribution

It develops a novel discontinuity-based bootstrap approach for BCFTs and applies it to compute specific correlators and OPE coefficients in an O(N) model at order epsilon.

Findings

Computed the ${ ext{phi} - ext{phi}^5$ bulk correlator.

Determined OPE coefficients up to $ ext{O}( ext{epsilon})$.

Validated the bootstrap method with explicit calculations.

Abstract

We consider a conformal field theory in the presence of a boundary, and explain how two-point correlators of mixed bulk-local operators can be bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the operator product expansion coefficients in either bootstrap channel. We apply this bootstrap technique to an $O(N)$-model in $d = 4 - \epsilon$ dimensions to find the $\phi - \phi^5$ bulk correlator and the corresponding operator product expansion coefficients upto $\mathcal{O}(\epsilon)$. Parts of this paper was first presented in my thesis.