Covariant perturbation theory and the Randall–Sundrum picture

Ezequiel Alvarez,Francisco D Mazzitelli

doi:10.1016/s0370-2693(01)00322-7

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.

Highlights

The effective action for quantum fields on a d-dimensional spacetime can be computed using a non-local expansion in powers of the curvature
When a 3-brane is inserted into AdS5, and for classical matter fields in the brane, the classical metric in five dimensions restricted to the brane reproduces the classical Newtonian potential plus the 1/r3 corrections
The meaning of Eq (9) is very simple: the first term corresponds to the classical propagation while the second contains the quantum corrections and is traced back to the non-local part of the action, Eq (5)

Summary

Introduction

The effective action for quantum fields on a d-dimensional spacetime can be computed using a non-local expansion in powers of the curvature. In two spacetime dimensions the quadratic term in the covariant perturbation theory reproduces the (exact) Polyakov action. The four-dimensional quadratic effective action has been used to compute the leading long distance 1/r3 corrections to the Newtonian potential [3]

Objectives

Results

Conclusion