Quantum $φ^4$ Theory in AdS${}_4$ and its CFT Dual

TL;DR

This work analyzes quantum φ^4 theory in Euclidean AdS_4 to compute holographic two- and four-point functions up to second order in the bulk coupling. The authors develop a position-space loop expansion with Schwinger-parameter techniques and a covariant UV/IR regularization to obtain analytic results for the anomalous dimensions of leading-twist double-trace operators for both Δ=1 and Δ=2 boundary conditions, including detailed expressions at one loop and beyond. They connect the bulk results to CFT data via conformal-block decompositions, extracting OPE coefficients and showing consistent leading-twist anomalous dimensions that match expectations from the dual boundary theory. The results illuminate how φ^4 interactions in AdS_4 contribute to the spectrum and OPE structure of the boundary CFT, providing a controlled example of loop corrections in AdS/CFT and informing higher-spin AdS duals with scalar sectors.

Abstract

We compute the two- and four-point holographic correlation functions up to the second order in the coupling constant for a scalar $φ^4$ theory in four-dimensional Euclidean anti-de Sitter space. Analytic expressions for the anomalous dimensions of the leading twist operators are found at one loop, both for Neumann and Dirichlet boundary conditions.