Analytic Bootstrap for Boundary CFT

TL;DR

This paper introduces an analytical method to solve bootstrap equations in boundary conformal field theories, enabling the calculation of correlators and CFT data, exemplified by the $ ext{Wilson-Fisher}$ fixed point in $ ext{phi}^4$ theory.

Contribution

It develops a novel analytical approach for boundary CFT bootstrap equations using the structure of Lorentzian correlators and discontinuities of conformal blocks.

Findings

Computed $raket{ ext{phi phi}}$ correlator at Wilson-Fisher fixed point to order $ ext{epsilon}^2$

Provided a new analytical framework for boundary CFT bootstrap equations

Enhanced understanding of boundary effects in conformal field theories

Abstract

We propose a method to analytically solve the bootstrap equation for two point functions in boundary CFT. We consider the analytic structure of the correlator in Lorentzian signature and in particular the discontinuity of bulk and boundary conformal blocks to extract CFT data. As an application, the correlator $\langle \phi \phi \rangle$ in $\phi^4$ theory at the Wilson-Fisher fixed point is computed to order $\epsilon^2$ in the $\epsilon$ expansion.