On Analytic Bootstrap for Interface and Boundary CFT

TL;DR

This paper develops an analytic bootstrap method for boundary and interface conformal field theories, deriving constraints on operator product expansion coefficients in perturbative Wilson-Fisher models with boundaries or interfaces.

Contribution

It introduces a general analytic bootstrap approach for boundary and interface CFTs, applying it to perturbative Wilson-Fisher theories to derive new constraints on OPE data.

Findings

Derived constraints on OPE coefficients in 4 - ε dimensions with φ^4 interactions.

Computed boundary OPE coefficients in 6 - ε dimensions for φ^3 theory.

Extended bootstrap techniques to non-unitary theories with boundary conditions.

Abstract

We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation of motion to the boundary operator expansion. The method presented in this paper is general, and it is illustrated in the context of perturbative Wilson-Fisher theories. In particular, we find constraints on the OPE coefficients for the conformal interface CFT in $4 - \epsilon$ dimensions (upto order $\mathcal{O}(\epsilon^2)$) with $\phi^4$-interactions in the bulk. We also compute the corresponding coefficients for the non-unitary $\phi^3$-theory in $6 - \epsilon$ dimensions in the presence of a conformal boundary equipped with either Dirichlet or Neumann boundary conditions upto order $\mathcal{O}(\epsilon)$, or an interface upto order $\mathcal{O}(\sqrt{\epsilon})$.