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.