Naturalness and UV sensitivity in Kaluza-Klein theories

Abstract

More than twenty years ago a paradigm emerged according to which a UV-insensitive Higgs mass $m_H$ and (more generally) a UV-insensitive Higgs effective potential $V_{1l}(\varphi )$ are obtained from higher-dimensional theories with compact extra dimensions and Scherk-Schwarz supersymmetry breaking. Since then, these ideas have been applied to different models of phenomenological interest, including recent applications to the dark energy problem. A thorough analysis of the framework on which such a paradigm is based allows us to show that a source of strong UV sensitivity for $m_H$ and $V_{1l}(\varphi )$, intimately connected to the non-trivial topology of these models' spacetime, was missed. The usual picture of the Scherk-Schwarz mechanism and its physical consequences need to be seriously reconsidered.

Comments: 37 pages, 10 figures