Gauge Mediation in F-Theory GUT Models

TL;DR

This paper presents a natural gauge-mediated supersymmetry-breaking framework within F-theory GUT models, solving the nd _{} problems by linking the Higgs sector, PQ symmetry, and SUSY-breaking scale, resulting in a low-energy effective theory resembling the 'sweet spot supersymmetry' scenario.

Contribution

It introduces a geometric mechanism in F-theory GUTs that naturally addresses the nd _{} problems and connects SUSY-breaking to  generation, with a low-energy effective action matching known supersymmetry scenarios.

Findings

A geometry that forbids t the GUT scale and links SUSY-breaking to  generation.

Realization of a D3-instanton triggered Polonyi model with exponentially suppressed scale.

Low-energy effective action consistent with the 'sweet spot supersymmetry' scenario.

Abstract

We study a simple framework for gauge-mediated supersymmetry-breaking in local GUT models based on F-theory 7-branes and demonstrate that a mechanism for solving both the \mu and \mu/B_{\mu} problems emerges in a natural way. In particular, a straightforward coupling of the messengers to the Higgs sector leads to a geometry which not only provides us with an approximate U(1)_{PQ} symmetry that forbids the generation of \mu at the GUT scale, it also forces the SUSY-breaking spurion field to carry a nontrivial PQ charge. This connects the breaking of SUSY to the generation of \mu so that the same scale enters both. Moreover, the messenger sector naturally realizes the D3-instanton triggered Polonyi model of arXiv:0808.1286 so this scale is exponentially suppressed relative to M_{GUT}. The effective action at low scales is in fact precisely of the form of the "sweet spot supersymmetry" scenario studied by Ibe and Kitano in arXiv:0705.3686.