A note on a gauge-gravity relation and functional determinants

TL;DR

This paper refines the gauge-gravity relation connecting one-loop effective actions for scalar and spinor fields in specific backgrounds, revealing new mappings in odd-dimensional AdS spaces and emphasizing the role of holographic trace anomalies.

Contribution

It provides a refined and extended gauge-gravity relation incorporating dimensional regularization and explores new mappings in odd-dimensional AdS spaces.

Findings

Complete mapping within dimensional regularization.

Small correction in even-dimensional AdS.

New subtle mapping in odd-dimensional AdS with holographic trace anomaly.

Abstract

We present a refinement of a recently found gauge-gravity relation between one-loop effective actions: on the gauge side, for a massive charged scalar in 2d dimensions in a constant maximally symmetric electromagnetic field; on the gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter space. The inclusion of the dimensionally regularized volume of AdS leads to complete mapping within dimensional regularization. In even-dimensional AdS, we get a small correction to the original proposal; whereas in odd-dimensional AdS, the mapping is totally new and subtle, with the `holographic trace anomaly' playing a crucial role.