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

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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.

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Authors and Affiliations

  1. Department of Physics, Syracuse University, Syracuse, NY, 13244, U.S.A.

    Dhagash Mehta

  2. Department of Mathematics, City University, London, EC1V 0HB, U.K.

    Yang-Hui He

  3. School of Physics, NanKai University, Tianjin, 300071, P.R. China

    Yang-Hui He

  4. Merton College, University of Oxford, Oxford, OX14JD, U.K.

    Yang-Hui He

  5. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, U.S.A.

    Jonathan D. Hauenstein

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  1. Dhagash Mehta
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  2. Yang-Hui He
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  3. Jonathan D. Hauenstein
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ArXiv ePrint: https://doi.org/1203.4235

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Mehta, D., He, YH. & Hauenstein, J.D. Numerical algebraic geometry: a new perspective on gauge and string theories. J. High Energ. Phys. 2012, 18 (2012). https://doi.org/10.1007/JHEP07(2012)018

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