A Simple Introduction to Grobner Basis Methods in String Phenomenology

TL;DR

This paper provides an accessible overview of Grobner basis algorithms and demonstrates their application in string phenomenology, including flux constraints, vacuum equations, and the MSSM vacuum space.

Contribution

It introduces the Grobner basis algorithm to the physics community and illustrates its utility through three practical examples in string phenomenology.

Findings

Grobner basis methods can constrain flux parameters.

They simplify equations for string vacua.

They enable computation of the MSSM vacuum space.

Abstract

In this talk I give an elementary introduction to the key algorithm used in recent applications of computational algebraic geometry to the subject of string phenomenology. I begin with a simple description of the algorithm itself and then give 3 examples of its use in physics. I describe how it can be used to obtain constraints on flux parameters, how it can simplify the equations describing vacua in 4d string models and lastly how it can be used to compute the vacuum space of the electroweak sector of the MSSM.