Quantum Stabilization of Compactified AdS_5
Walter D. Goldberger, Ira Z. Rothstein
TL;DR
The paper investigates whether quantum fluctuations in a compactified AdS$_5$ setup with two branes can stabilize the radion. It computes the one-loop effective potential from fields on the TeV brane and in the bulk using dimensional regularization and zeta-function techniques, with careful covariant renormalization. The TeV-brane contributions renormalize brane tensions and do not generate a stabilizing $a$-dependent term, while bulk contributions yield $a$-dependent pieces that are either absorbed into counterterms or are power-suppressed for large $kr_c$, offering no natural mechanism to stabilize the hierarchy. Consequently, a classical stabilization mechanism, such as Goldberger-Wise, remains necessary, and the analysis clarifies regulator-covariance issues that previously led to conflicting results.
Abstract
We investigate the role of quantum fluctuations in the system composed of two branes bounding a region of AdS. It is shown that the modulus effective potential generated by quantum fluctuations of both brane and bulk fields is incapable of stabilizing the space naturally at the separation needed to generate the hierarchy. Consequently, a classical stabilization mechanism is required. We describe the proper method of regulating the loop integrals and show that, for large brane separation, the quantum effects are power suppressed and therefore have negligible affects on the bulk dynamics once a classical stabilization mechanism is in place.