Quantum self-consistency ofAdS×Σbrane models

Abstract

Continuing our previous work, we consider a class of higher dimensional brane models with the topology of ${\mathrm{AdS}}_{{D}_{1}+1}\ifmmode\times\else\texttimes\fi{}\ensuremath{\Sigma},$ where $\ensuremath{\Sigma}$ is a one-parameter compact manifold and two branes of codimension one are located at the orbifold fixed points. We consider a setup where such a solution arises from Einstein-Yang-Mills theory and evaluate the one-loop effective potential induced by gauge fields and by a generic bulk scalar field. We show that this type of brane model resolves the gauge hierarchy between the Planck and electroweak scales through redshift effects due to the warp factor ${a=e}^{\ensuremath{-}\ensuremath{\pi}\mathrm{kr}}.$ The value of a is then fixed by minimizing the effective potential. We find that, as in the Randall-Sundrum case, the gauge field contribution to the effective potential stabilizes the hierarchy without fine-tuning as long as the Laplacian ${\ensuremath{\Delta}}_{\ensuremath{\Sigma}}$ on $\ensuremath{\Sigma}$ has a zero eigenvalue. Scalar fields can stabilize the hierarchy depending on the mass and the nonminimal coupling. We also address the quantum self-consistency of the solution, showing that the classical brane solution is not spoiled by quantum effects.