Quantum self-consistency of $AdS \times \Sigma$ brane models

TL;DR

This paper investigates higher-dimensional $AdS imes ext{compact manifold}$ brane models, demonstrating how gauge fields and scalars stabilize the hierarchy between fundamental scales through quantum effects, ensuring the model's self-consistency.

Contribution

It extends previous work by analyzing quantum self-consistency and hierarchy stabilization in $AdS imes ext{compact}$ brane models derived from Einstein-Yang-Mills theory.

Findings

Gauge field contributions stabilize the hierarchy without fine-tuning.

Scalar fields can also stabilize the hierarchy depending on parameters.

The classical brane solution remains stable under quantum corrections.

Abstract

Continuing on our previous work, we consider a class of higher dimensional brane models with the topology of $AdS_{D_1+1} \times \Sigma$, where $\Sigma$ is a one-parameter compact manifold and two branes of codimension 1 are located at the orbifold fixed points. We consider a set-up 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 models resolves the gauge hierarchy between the Planck and electroweak scales through redshift effects due to the warp factor $a=e^{-\pi kr}$. 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 stabilises the hierarchy without fine-tuning as long as the laplacian $\Delta_\Sigma$ on $\Sigma$ has a zero eigenvalue. Scalar fields can stabilise the hierarchy depending on the mass and the non-minimal coupling. We also address the quantum self-consistency of the solution, showing that the classical brane solution is not spoiled by quantum effects.