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Veronese Geometry and the Electroweak Vacuum Moduli Space

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arxiv 1402.3312 v1 pith:HJDZ5MOZ submitted 2014-02-13 hep-th hep-phmath.AG

Yang-Hui He , Vishnu Jejjala , Cyril Matti , Brent D. Nelson This is my paper · ORCID
classification hep-thhep-phmath.AG
keywords geometryelectroweakvacuumveronesemodulispacesurfacealgebraic
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We explain the origin of the Veronese surface in the vacuum moduli space geometry of the MSSM electroweak sector. While this result appeared many years ago using techniques of computational algebraic geometry, it has never been demonstrated analytically. Here, we present an analytical derivation of the vacuum geometry of the electroweak theory by understanding how the F- and D-term relations lead to the Veronese surface. We moreover give a detailed description of this geometry, realising an extra branch as a zero-dimensional point when quadratic Higgs lifting deformations are incorporated into the superpotential.

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  1. Vacuum Geometry of the Standard Model

    hep-th 2025-06 conditional novelty 7.0 of 10

    The vacuum moduli space of the MSSM is shown to consist of three rational components of dimensions 1, 15, and 29 via Gröbner basis computations.

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