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Advances in High Energy Physics
Volume 2011 (2011), Article ID 217035, 12 pages
http://dx.doi.org/10.1155/2011/217035
Review Article

A Simple Introduction to Gröbner Basis Methods in String Phenomenology

Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK

Received 3 February 2011; Accepted 13 February 2011

Academic Editor: Yang-Hui He

Copyright © 2011 James Gray. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.