Exponentially Small Couplings and the Hierarchy Problem

TL;DR

The paper introduces a string-inspired mechanism using a fifth dimension to generate an exponentially small hierarchy between symmetry breaking scales, addressing the hierarchy problem.

Contribution

It presents a novel stringy approach involving a fifth dimension and supersymmetry to produce exponentially suppressed symmetry breaking scales.

Findings

Achieves a hierarchy suppression factor dependent exponentially on the fifth dimension length.

Demonstrates a mechanism for generating small electroweak scales from larger GUT scales.

Provides a model where supersymmetric flat directions lead to exponentially small gauge symmetry breaking.

Abstract

We propose a stringy mechanism whereby a large hierarchy between symmetry breaking scales is generated. This mechanism is based upon the existence of a fifth dimension compactified on a segment. We focus on a simple supersymmetric model with one massless Higgs field in the 3 of SU(3) and another one in the $\bar 3$ on each four dimensional end-point of the fifth dimension. Along supersymmetric flat directions the gauge symmetry is broken down to SU(2) due to the vacuum expectation value of the Higgs fields on one of the end points. The remaining massless mode on the other end point acquires a potential due to a massive five dimensional state propagating between the end points. This potential breaks the SU(2) symmetry at an exponentially suppressed scale compared to the SU(3) breaking scale. The suppression factor depends exponentially on the mass M of the massive state and the length $\pi R$ of the fifth dimension. For reasonably large values of the length scale R one can achieve a factor of order $M_{W}/M_GUT}$.