A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction

TL;DR

This paper demonstrates that for scalar quantum fields with exponential interaction on Euclidean hyperbolic space, the infra-red limit of the boundary generating functional becomes trivial, revealing a fundamental simplification in the AdS/CFT correspondence.

Contribution

It introduces a novel approach using decoupling inequalities to analyze the infra-red limit in Euclidean hyperbolic space with exponential interactions.

Findings

Infra-red limit of the boundary generating functional is trivial.

Decoupling inequalities effectively analyze boundary behavior.

Results apply to scalar quantum fields with exponential interaction.

Abstract

We consider scalar quantum fields with exponential interaction on Euclidean hyperbolic space $\mathbb{H}^2$ in two dimensions. Using decoupling inequalities for Neumann boundary conditions on a tessellation of $\mathbb{H}^2$, we are able to show that the infra-red limit for the generating functional of the conformal boundary field becomes trivial.