Radius Stabilization by Two-Loop Casimir Energy

Abstract

It is well known that the Casimir energy of bulk fields induces a non-trivial potential for the compactification radius of higher-dimensional field theories. On dimensional grounds, the 1-loop potential is ~ 1/R^4. Since the 5d gauge coupling constant g^2 has the dimension of length, the two-loop correction is ~ g^2/R^5. The interplay of these two terms leads, under very general circumstances (including other interacting theories and more compact dimensions), to a stabilization at finite radius. Perturbative control or, equivalently, a parametrically large compact radius is ensured if the 1-loop coefficient is small because of an approximate fermion-boson cancellation. This is similar to the perturbativity argument underlying the Banks-Zaks fixed point proposal. Our analysis includes a scalar toy model, 5d Yang-Mills theory with charged matter, the examination of S^1 and S^1/Z_2 geometries, as well as a brief discussion of the supersymmetric case with Scherk-Schwarz SUSY breaking. 2-Loop calculability in the S^1/Z_2 case relies on the log-enhancement of boundary kinetic terms at the 1-loop level.