He, Y.-H.Jejjala, V.Matti, C.Nelson, B.D.2017-04-182017-04-182016-03He, Y.H. et.al. 2016. Testing R-parity with geometry. Journal of High Energy Physics 2016 (3) : Article number 79.1126-6708 (Print)1029-8479 (Online)http://hdl.handle.net/10539/22395We 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 (Formula presented.) , generating vacuum moduli spaces equivalent to those with a fundamental bilinear.en© 2016 He, Y.-H. et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).Supersymmetric Effective TheoriesSupersymmetric gauge theorySYMMETRY-BREAKINGArticle