Sakharov's induced gravity on the AdS background: SM scale as inverse mass parameter of the Schwinger-DeWitt expansion

TL;DR

This paper explores how quantum effects induce gravity on an AdS background within the Randall-Sundrum model, proposing a novel method to analyze the effective action and its implications for brane stabilization and the hierarchy problem.

Contribution

It introduces a new auxiliary mass method for resumming the Schwinger-DeWitt expansion in AdS space, linking the IR-brane position to the inverse mass parameter and addressing stabilization.

Findings

Induced vacuum energy density matches stress-energy tensor VEV.

Potential has a non-trivial extremum for brane stabilization.

Naive parameter matching is insufficient; a quantum self-consistency principle is proposed.

Abstract

One loop quantum effective action W of scalar field 'living' on the AdS background of the Randall-Sundrum model is defined here by now popular way which excludes bulk UV divergencies; thus induced Planck mass is given not by the UV regularization parameter, like in Sakharov's pioneer work, but by the location of the UV-cut of AdS space. Resummation of Schwinger-DeWitt expansion of the action W is performed by the novel 'auxiliary mass' method. The inverse mass squared parameter of this expansion is determined by the location of the 'visible' IR-brane of the RS-model. Obtained expression for induced vacuum energy density coincides with the independently calculated VEV of the stress-energy tensor. Corresponding potential in 4 dimensions possesses a non-trivial extremum which hopefully will permit us to stabilize IR brane and hence to fix the observed small value of mass hierarchy in analogy with the Coleman-Weinberg mechanism. It is demonstrated that naive equating of values of the induced Planck mass and vacuum energy density to those of the RS-model determines otherwise arbitrary constants of the model. A principle of quantum self-consistency generalizing this approach is proposed.