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Numerical algebraic geometry: a new perspective on gauge and string theories

  • Dhagash Mehta
  • Yang-Hui HeEmail author
  • Jonathan D. Hauenstein
Article

Abstract

There is a rich interplay between algebraic geometry and string and gauge theories which has been recently aided immensely by advances in computational algebra. However, symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these shortcomings. The so-called ‘embarrassing parallelizability’ allows us to solve many problems and extract physical information which elude symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.

Keywords

Strings and branes phenomenology Supersymmetry Phenomenology 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Dhagash Mehta
    • 1
  • Yang-Hui He
    • 2
    • 3
    • 4
    Email author
  • Jonathan D. Hauenstein
    • 5
  1. 1.Department of PhysicsSyracuse UniversitySyracuseU.S.A.
  2. 2.Department of MathematicsCity UniversityLondonU.K.
  3. 3.School of PhysicsNanKai UniversityTianjinP.R. China
  4. 4.Merton CollegeUniversity of OxfordOxfordU.K.
  5. 5.Department of MathematicsTexas A&M UniversityCollege StationU.S.A.

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