Interacting conformal scalar in a wedge

TL;DR

This paper analyzes two-point functions in a conformal field theory near a wedge with intersecting boundaries, computing anomalous dimensions via Dyson-Schwinger equations and Feynman diagrams in various dimensions.

Contribution

It introduces a method to compute two-point functions and anomalous dimensions in wedge geometries using Dyson-Schwinger equations in $d=4- ext{epsilon}$ and $d=3- ext{epsilon}$ dimensions.

Findings

Computed two-point functions near a wedge with intersecting boundaries.

Extracted anomalous dimensions from correlators.

Validated results with Feynman diagram calculations.

Abstract

We study a class of two-point functions in a conformal field theory near a wedge. This is a set-up with two boundaries intersecting at an angle $\theta$. We compute it as a solution to the Dyson-Schwinger equation of motion for a quartic interaction in the $d=4-\epsilon$ bulk and in the $d=3-\epsilon$ boundary, up to order $\mathcal{O}(\epsilon)$. We have extracted the anomalous dimensions from such correlators and we have complemented them with Feynman diagrams computations.