A Gauge-Gravity Relation in the One-loop Effective Action

TL;DR

This paper uncovers a novel gauge-gravity relation by expressing one-loop effective actions for different fields in AdS space and electromagnetic backgrounds using the same special function, revealing a deep non-perturbative connection.

Contribution

It establishes a new gauge-gravity relation linking effective actions in AdS space and electromagnetic backgrounds through a shared mathematical function.

Findings

Effective actions are expressed in terms of the same gamma function.

The relation links gravitational curvature to electromagnetic field strength.

Implication for non-perturbative gauge-gravity dualities.

Abstract

We identify an unusual new gauge-gravity relation: the one-loop effective action for a massive spinor in 2n dimensional AdS space is expressed in terms of precisely the same function [a certain multiple gamma function] as the one-loop effective action for a massive charged scalar in 4n dimensions in a maximally symmetric background electromagnetic field [one for which the eigenvalues of F_{\mu\nu} are maximally degenerate, corresponding in 4 dimensions to a self-dual field, equivalently to a field of definite helicity], subject to the identification F^2 <-> \Lambda, where \Lambda is the gravitational curvature. Since these effective actions generate the low energy limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a nontrivial gauge-gravity relation at the non-perturbative level and at the amplitude level.