Runaway relaxion monodromy

Abstract

We examine the relaxion mechanism in string theory. An essential feature is that an axion winds over N ≫ 1 fundamental periods. In string theory realizations via axion monodromy, this winding number corresponds to a physical charge carried by branes or fluxes. We show that — in the context of NS5-brane axion monodromy — this charge backreacts on the compact space, ruining the structure of the relaxion action. In particular, the barriers generated by strong gauge dynamics have height ∝ e−N , so the relaxion does not stop when the Higgs acquires a vev. Backreaction of monodromy charge can therefore spoil the relaxion mechanism. We comment on the limitations of technical naturalness arguments in this context.