One-loop effective potential from higher-dimensional AdS black holes

TL;DR

This paper calculates the quantum effects of bulk fields in a higher-dimensional AdS black hole background, showing they induce a positive cosmological constant on a brane-world universe.

Contribution

It provides an explicit calculation of the one-loop effective potential in a brane-world model with a higher-dimensional AdS black hole using zeta regularisation.

Findings

Bulk quantum fields generate a positive cosmological constant.

The effective potential is explicitly computed in the large mass regime.

The results support the viability of brane-world models with positive cosmological constant.

Abstract

We study the quantum effects in a brane-world model in which a positive constant curvature brane universe is embedded in a higher-dimensional bulk AdS black hole, instead of the usual portion of the AdS$_5$. By using zeta regularisation, in the large mass regime, we explicitly calculate the one-loop effective potential due to the bulk quantum fields and show that it leads to a non-vanishing cosmological constant, which can definitely acquire a positive value.