Vacuum Geometry and the Search for New Physics

TL;DR

This paper introduces a novel approach using vacuum space geometry to guide phenomenological models, providing new computational tools and insights into the structure of supersymmetric theories and their connection to string physics.

Contribution

It presents new algorithmic methods for analyzing the geometric properties of vacuum spaces in supersymmetric gauge theories and applies them to the MSSM.

Findings

Geometric fragility in the moduli space influences superpotential deformations.

Special vacuum geometry may indicate underlying string physics.

The methods facilitate efficient computation of vacuum space properties.

Abstract

We propose a new guiding principle for phenomenology: special geometry in the vacuum space. New algorithmic methods which efficiently compute geometric properties of the vacuum space of N=1 supersymmetric gauge theories are described. We illustrate the technique on subsectors of the MSSM. The fragility of geometric structure that we find in the moduli space motivates phenomenologically realistic deformations of the superpotential, while arguing against others. Special geometry in the vacuum may therefore signal the presence of string physics underlying the low-energy effective theory.