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

TL;DR

This paper calculates holographic correlation functions for a scalar ^4 theory in AdS4, providing analytic results for anomalous dimensions of operators at one loop, advancing understanding of AdS/CFT correspondence.

Contribution

It offers the first analytic computation of two- and four-point functions and anomalous dimensions in ^4 theory in AdS4 at second order in coupling.

Findings

Analytic expressions for two- and four-point functions up to second order.

Anomalous dimensions of leading twist operators computed at one loop.

Results apply to both Neumann and Dirichlet boundary conditions.

Abstract

We compute the two- and four-point holographic correlation functions up to the second order in the coupling constant for a scalar $\phi^4$ 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.