Ultraviolet phenomena in AdS self-interacting quantum field theory

TL;DR

This paper investigates one-loop corrections in AdS $$ field theory, revealing non-local counterterms that preserve AdS symmetry and discussing differences between Euclidean and Lorentzian calculations.

Contribution

It demonstrates the existence of non-local counterterms in AdS $$ $$ field theory and explains signature-dependent calculation differences.

Findings

Non-local counterterms respect AdS isometry.

Differences between Euclidean and Lorentzian calculations are significant.

Results are applicable to various non-conformal AdS theories.

Abstract

We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $\phi^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general and applicable to other (non-conformal) AdS field theories. We also explain why calculations in Euclidean and Lorentzian signatures should differ even at the leading order in non globaly hyperbolic manifolds.