Interacting conformal scalar in a wedge

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.

34 pages, modified section 3.2.1, reference added

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• Casimir Effect and Holographic Dual of Wedges
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations