Flux compactifications and naturalness

TL;DR

This paper demonstrates a mechanism in higher-dimensional theories where coupling a scalar to an infinite tower of states cancels quantum corrections, preserving shift symmetry and addressing naturalness issues like the hierarchy problem.

Contribution

It introduces a model where an infinite tower of states from a compactified higher-dimensional theory cancels quantum divergences, maintaining scalar shift symmetry.

Findings

Quantum corrections sum to zero, preventing large scalar masses.

Shift symmetry remains intact despite gauge and Yukawa interactions.

Provides a potential solution to the hierarchy problem.

Abstract

Free massless scalars have a shift symmetry. This is usually broken by gauge and Yukawa interactions, such that quantum corrections induce a quadratically divergent mass term. In the Standard Model this leads to the hierarchy problem of the electroweak theory, the question why the Higgs mass is so much smaller than the Planck mass. We present an example where a large scalar mass term is avoided by coupling the scalar to an infinite tower of massive states which are obtained from a six-dimensional theory compactified on a torus with magnetic flux. The series of divergent quantum corrections adds up to zero, and we show explicitly that the shift symmetry of the scalar is preserved in the effective four-dimensional theory despite the presence of gauge and Yukawa interaction terms.