Scalar field on AdS: quantum one loop "in one line"

TL;DR

This paper presents a simplified method to compute quantum one-loop potentials in Randall-Sundrum models using Barvinsky-Nesterov and Gelfand-Yaglom techniques, providing explicit formulas for energy differences and induced constants.

Contribution

It introduces a straightforward integral expression for quantum energies in RS models and derives compact formulas for induced physical constants, addressing IR-divergences in one-brane scenarios.

Findings

Explicit integral formulas for quantum energy differences.

Compact expressions for induced Planck mass and gauge couplings.

Identification of IR-divergences in Schwinger-DeWitt expansion for one-brane models.

Abstract

It is shown that quantum one-loop potentials of the bulk fields in the Randall and Sundrum (RS) model may be immediately expressed in integrals with use of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants. Simple expression is obtained for the UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary condition in one-brane and two-brane RS-models. Compact formula for Schwinger-DeWitt expansion gives values of induced Planck mass and induced gauge coupling constant in transverse space. S-DW expansion is plagued by IR-divergences in one-brane RS-model and makes sense in two-brane model.