Computational Algebraic Geometry in String and Gauge Theory

Yang-Hui He,Andre Lukas,Philip Candelas,Amihay Hanany,Burt Ovrut

doi:10.1155/2012/431898

Abstract

1 Department of Mathematics, City University London, London EC1V 0HB, UK 2 School of Physics, Nan Kai University, TianJin 300071, China 3 Merton College, University of Oxford, Oxford OX1 4JD, UK 4 Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK 5 Department of Physics, Imperial College, London SW7 2AZ, UK 6 Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK 7 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 191046395, USA

Highlights

The last few years have witnessed a rapid development in algebraic geometry, computer algebra, and string and field theory, as well as fruitful cross-fertilization amongst them
Applications of once specialized mathematical topics such as Grobner bases, sheaf cohomology, scheme theory, and Hilbert series are quickly becoming indispensible tools in theoretical physics, from topics ranging from AdS/CFT to string phenomenology, from supersymmetric gauge theory to Calabi-Yau compactifications, and so forth
Gray is a review on the most important subject in computational and algorithmic algebraic geometry: the Grobner basis. It illustrates how this can be used in string phenomenology and gives some concrete examples ranging from flux parameter to vacuum spaces

Summary

Introduction

The last few years have witnessed a rapid development in algebraic geometry, computer algebra, and string and field theory, as well as fruitful cross-fertilization amongst them. Editorial Computational Algebraic Geometry in String and Gauge Theory Applications of once specialized mathematical topics such as Grobner bases, sheaf cohomology, scheme theory, and Hilbert series are quickly becoming indispensible tools in theoretical physics, from topics ranging from AdS/CFT to string phenomenology, from supersymmetric gauge theory to Calabi-Yau compactifications, and so forth. Gray is a review on the most important subject in computational and algorithmic algebraic geometry: the Grobner basis.

Results

Conclusion