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.
Highlights
Why is the Higgs mass so small? Graham, Kaplan, and Rajendran (GKR) have proposed a novel solution to the electroweak hierarchy problem, the relaxion mechanism, in which the evolution of an axion field φ drives the Higgs mass mh to relax dynamically to a value much smaller than the cutoff, |m2h| M 2 [1]
The large field excursions required by the mechanism, while technically natural in effective field theory, turn out to be source terms in string theory! Winding an axion φ over N 1 fundamental periods leads to the accumulation of N units of monodromy charge, providing a large source term in ten dimensions
Could a portion of the observed hierarchy between the weak scale and the Planck scale be a consequence of dynamical relaxation of the Higgs mass during cosmological evolution? This striking idea is the core of the relaxion mechanism [1]
Summary
Why is the Higgs mass so small? Graham, Kaplan, and Rajendran (GKR) have proposed a novel solution to the electroweak hierarchy problem, the relaxion mechanism, in which the evolution of an axion field φ drives the Higgs mass mh to relax dynamically to a value much smaller than the cutoff, |m2h| M 2 [1]. Winding an axion φ over N 1 fundamental periods leads to the accumulation of N units of monodromy charge, providing a large source term in ten dimensions This changes the shape of the compactification and alters the couplings of the effective theory, eliminating the barrier that is needed to stop the relaxion once the Higgs acquires a vev. The root of the problem is that new states linked to the monodromy charge, which are too massive in the initial configuration to be visible, are eventually drawn below the cutoff M These new light states induce changes in the couplings of the effective theory. The gauge coupling gYM of the gauge theory that generates the stopping potential receives a correction δgY−M2 ∼ N This leads to an exponential suppression of the stopping potential, with barrier heights ∼ e−N , and to a runaway relaxion. This problem persists even in the limit in which the relaxion shift symmetry appears to be restored
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