Conformal Bootstrap near the edge

TL;DR

This paper develops a conformal bootstrap framework for boundary conformal field theories near intersecting boundaries forming a co-dimension 2 edge, deriving crossing equations and solving them analytically in simple cases.

Contribution

It introduces a bootstrap approach for CFTs near boundary intersections, deriving and solving crossing equations involving bulk and edge correlators.

Findings

Derived conformal block expansions for bulk and edge correlators.

Established crossing equations for boundary intersections.

Solved the equations analytically for simple free-field cases.

Abstract

We propose a bootstrap program for CFTs near intersecting boundaries which form a co-dimension 2 edge. We describe the kinematical setup and show that bulk 1-pt functions and bulk-edge 2-pt functions depend on a non-trivial cross-ratio and on the angle between the boundaries. Using the boundary OPE (BOE) with respect to each boundary, we derive two independent conformal block expansions for these correlators. The matching of the two BOE expansions leads to a crossing equation. We analytically solve this equation in several simple cases, notably for a free bulk field, where we recover Feynman-diagrammatic results by Cardy.