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Numerical elimination and moduli space of vacua

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Abstract

We propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we develop a powerful, efficient, and parallelizable algorithm to extract important information such as the dimension, branch structure, Hilbert series and subsequent operator counting, as well as variation according to coupling constants and mass parameters. We illustrate this method on a host of examples from gauge theory, string theory, and algebraic geometry.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, U.S.A

    Jonathan Hauenstein

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

    Yang-Hui He

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

    Yang-Hui He

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

    Yang-Hui He

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

    Dhagash Mehta

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  1. Jonathan Hauenstein
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  2. Yang-Hui He
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ArXiv ePrint: 1210.6038

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Hauenstein, J., He, YH. & Mehta, D. Numerical elimination and moduli space of vacua. J. High Energ. Phys. 2013, 83 (2013). https://doi.org/10.1007/JHEP09(2013)083

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