Quantum (In)Stability of a Brane-World AdS${}_{\mathbf{5}}$ Universe at Nonzero Temperature

We consider the quantum effects of bulk matter (scalars, spinors) in the Randall-Sundrum AdS${}_5$ brane-world at nonzero temperature. The thermodynamic energy (modulus potential) is evaluated at low and high temperatures. This potential has an extremum which could be a minimum in some cases (for example, for a single fermion). That suggests a new dynamical mechanism to stabilize the thermal AdS${}_5$ brane-world. It is shown that the brane separation required to solve the hierarchy scale problem may occur at a quite low temperature. A natural generalization in terms of the AdS/CFT correspondence (through the supergravity thermal contribution) is also possible.