A Simple Introduction to Grobner Basis Methods in String Phenomenology

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.

13 pages, Prepared for Mathematical Challenges in String Phenomenology, ESI Vienna, Austria, Oct 6-15, 2008

References in corpus (20)

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• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
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• Can String Theory Predict the Weinberg Angle?
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials

Cited by in corpus (10)

• Heterotic Line Bundle Standard Models
• The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications
• Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories
• Complete Intersection Moduli Spaces in N=4 Gauge Theories in Three Dimensions
• Numerical Polynomial Homotopy Continuation Method and String Vacua
• Calabi-Yau Manifolds with Large Volume Vacua
• Numerical Analyses on Moduli Space of Vacua
• Jumping Spectra and Vanishing Couplings in Heterotic Line Bundle Standard Models
• Veronese Geometry and the Electroweak Vacuum Moduli Space
• Testing R-parity with Geometry