The one-loop quantum effective action $W$ of the scalar field “living” on the AdS background of the Randall-Sundrum (RS) model has been defined by a now-popular way which excludes bulk UV divergencies; thus, the 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 the 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. The obtained expression for the induced vacuum energy density coincides with the independently calculated VEV of the stress-energy tensor; the corresponding potential in four dimensions possesses a nontrivial extremum which hopefully will permit us to stabilize the IR brane and hence to fix the observed small value of the 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.

• Received 7 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.065007