Conformal Manifolds with Boundaries or Defects

TL;DR

This paper investigates the structure of conformal manifolds in conformal field theories with boundaries or defects, deriving constraints on operator expansions and confirming the existence of marginal couplings through explicit examples.

Contribution

It introduces a conformal perturbation theory approach to analyze boundary and defect conformal manifolds, deriving new constraints and confirming vanishing beta-functions in specific models.

Findings

Derived constraints on boundary operator product expansion coefficients.

Confirmed vanishing beta-functions in several explicit examples.

Validated results with existing literature where applicable.

Abstract

We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions that need to be satisfied for the existence of marginal couplings. We present several explicit examples where we confirm that $\beta$-functions vanish using a position space regularization, differential regularization. Where possible, we confirm that our $\beta$-function results agree with the existing literature.