Covariant perturbation theory and the Randall-Sundrum picture

TL;DR

This paper demonstrates that the non-local effective action for conformal quantum fields in a d-dimensional spacetime is equivalent to a classical gravity action in an AdS_{d+1} space restricted to a brane, linking quantum corrections to a higher-dimensional classical picture.

Contribution

It establishes a direct equivalence between the non-local quantum effective action and a classical gravity action in higher-dimensional AdS space for conformal fields.

Findings

Non-local effective action matches the classical AdS_{d+1} gravity action on a brane.

Provides a new perspective on quantum corrections via higher-dimensional classical theories.

Generalizes previous results on quantum corrections to gravitational potentials.

Abstract

The effective action for quantum fields on a $d$-dimensional spacetime can be computed using a non local expansion in powers of the curvature. We show explicitly that, for conformal fields and up to quadratic order in the curvature, the non local effective action is equivalent to the $d+1$ action for classical gravity in $AdS_{d+1}$ restricted to a $d-1$-brane. This generalizes previous results about quantum corrections to the Newtonian potential and provides an alternative method for making local a non-local effective action. The equivalence can be easily understood by comparing the Kallen-Lehmann decomposition of the classical propagator with the spectral representation of the non local form factors in the quantum effective action.