Exploring the Vacuum Geometry of N=1 Gauge Theories

TL;DR

This paper introduces an efficient algebraic geometry-based method to explicitly compute the vacuum space of N=1 gauge theories, linking geometric properties to phenomenological insights in high-energy physics.

Contribution

The authors develop a novel algorithmic approach for analyzing vacuum geometries in N=1 gauge theories, with applications to the MSSM and electroweak sector.

Findings

Explicit vacuum space descriptions for MSSM subsectors

Geometric analysis of electroweak theory vacuum space

Method can exclude certain high-energy physics models

Abstract

Using techniques of algorithmic algebraic geometry, we present a new and efficient method for explicitly computing the vacuum space of N=1 gauge theories. We emphasize the importance of finding special geometric properties of these spaces in connecting phenomenology to guiding principles descending from high-energy physics. We exemplify the method by addressing various subsectors of the MSSM. In particular the geometry of the vacuum space of electroweak theory is described in detail, with and without right-handed neutrinos. We discuss the impact of our method on the search for evidence of underlying physics at a higher energy. Finally we describe how our results can be used to rule out certain top-down constructions of electroweak physics.