The Higgs Sector on a Two-Sheeted Space Time

Abstract

We present a general formalism based on the framework of non-commutative geometry, suitable to the study the standard model of electroweak interactions, as well as that of more general gauge theories. Left- and right-handed chiral fields are assigned to two different sheets of space-time (a discretized version of Kaluza-Klein theory). Scalar Higgs fields find themselves treated on the same footing as the gauge fields, resulting in spontaneous symmetry breaking in a natural and predictable way. We first apply the formalism to the Standard Model, where one can predict the Higgs mass and the top Yukawa coupling. We then study the left-right symmetric model, where we show that this framework imposes constraints on the type and coefficients of terms appearing in the Higgs potential.