Abstract
We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new vacuum manifolds are identified; we thereby investigate the geometrical implication of theories which display a manifest matter parity (or R-parity) via the distinction between leptonic and Higgs doublets, and of the lepton number assignment of the right-handed neutrino fields.
We find that the traditional R-parity assignments of the MSSM more readily accommodate the neutrino see-saw mechanism with non-trivial geometry than those superpotentials that violate R-parity. However there appears to be no geometrical preference for a fundamental Higgs bilinear in the superpotential, with operators that violate lepton number, such as \( \nu H\overline{H} \), generating vacuum moduli spaces equivalent to those with a fundamental bilinear.
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He, YH., Jejjala, V., Matti, C. et al. Testing R-parity with geometry. J. High Energ. Phys. 2016, 79 (2016). https://doi.org/10.1007/JHEP03(2016)079
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DOI: https://doi.org/10.1007/JHEP03(2016)079