Exceptional Lie Superalgebras, Invariant Morphisms, and a Second-Gauged Standard Model

Abstract

Degenerate modules of the exceptional infinite-dimensional simple Lie superalgebras vle(3|6), ksle(5|10) and mb(3|8) have recently been constructed by Kac and Rudakov, and by Grozman, Leites and Shchepochkina. I rederive their results using a formalism which is contragredient to theirs; instead of finding singular vectors in induced modules, I build reducible tensor modules ("forms") from elementary differentials. There is a discrepancy between my result for ksle(5|10) and Kac' and Rudakov's one. Since the grade zero subalgebra of vle(3|6) and mb(3|8) is sl(3)+sl(2)+gl(1), gauge theories based on these algebras can be viewed as a "second-gauged" version of the standard model, where the rigid sl(3)+sl(2)+gl(1), symmetry is made local not only in spacetime ("first gauging"), but in the internal directions as well. An attempt to construct such a second-gauged theory is presented. Some predictions regarding the fermion spectrum, absense of new gauge bosons, and CP violation follow immediately.