Simple way to calculate UV-finite one-loop quantum energy in Randall-Sundrum model

TL;DR

This paper introduces a simplified method using Barvinsky-Nesterov and Gelfand-Yaglom techniques to efficiently compute UV-finite differences of one-loop quantum energies in Randall-Sundrum models, generalizing previous results.

Contribution

It presents a compact, general approach to calculate one-loop quantum energies in RS-models for arbitrary boundary conditions, extending prior specific calculations.

Findings

Derived compact expressions for UV-finite energy differences.

Generalized Gubser and Mitra's results to arbitrary boundary conditions.

Enabled quick calculation of one-loop energies in two-brane RS-models.

Abstract

The surprising simplicity of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants permits to obtain compact expressions for UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary conditions. This result generalizes Gubser and Mitra calculation for particular case of difference of "regular" and "irregular" one-loop energies in one-brane RS-model. Approach developed in the paper also allows to get "in one line" the one-loop quantum energies in two-brane RS-model. The relationship between "one-loop" expressions corresponding to mixed Robin and to double-trace asymptotic boundary conditions is traced.