Journal Article

Composite operators near the boundary

Procházka, Vladimír, Söderberg, Alexander

2020

Overview

A bstract We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. We apply the formalism to a scalar field theory in d = 3 − 𝜖 dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using 𝜖 − expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress tensor decouples at the fixed point in accordance with Cardy’s condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this fixed point for various values of 𝜖.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: Boundary Quantum Field Theory / Classical and Quantum Gravitation / Conformal Field Theory / Couplings / Critical phenomena / Elementary Particles / Energy / Field theory / Fixed points (mathematics) / High energy physics / Mathematical analysis / Operators (mathematics) / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / Renormalization Group / Renormalization group methods / Scalars / String Theory / Tensors