Standard Model Plethystics

Abstract

We study the vacuum geometry prescribed by the gauge invariant operators of the MSSM via the Plethystic Programme. This is achieved by using several tricks to perform the highly computationally challenging Molien-Weyl integral, from which we extract the Hilbert series, encoding the invariants of the geometry at all degrees. The fully refined Hilbert series is presented as the explicit sum of 1422 rational functions. We found a good choice of weights to unrefine the Hilbert series into a rational function of a single variable, from which we can read off the dimension and the degree of the vacuum moduli space of the MSSM gauge invariants. All data in Mathematica format are also presented.

arXiv commentTypos corrected

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Cited by in corpus (3)

• Flavor Invariants and Renormalization-group Equations in the Leptonic Sector with Massive Majorana Neutrinos
• Hilbert Series, Machine Learning, and Applications to Physics
• Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases