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Standard Model Plethystics
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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.
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The Vacuum Moduli Space of the Minimal Supersymmetric Standard Model
The full classical vacuum moduli space of the MSSM is computed: three rational components of dimensions 1, 15 and 29 without neutrinos, and one component when neutrinos are added.
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