Are physical cutoffs required in spontaneous gauge symmetry breaking?

Abstract

Triviality of scalar field theories makes the naive version of spontaneous symmetry breaking (SSB) questionable. We study whether the problem of triviality is removed by other sectors of a theory without a need for physical cutoffs (or embedding scales) in the largeN limit. The problem for a similar situation with finiteN can be understood as being some deviation from the largeN limit. This point of view shows the systematic of the problem in a nice way. In consequence the result can be used as an aid for understanding or avoiding such problems in other models. Additionally it is shown that the formal asymmetry of SSB where scalars are just needed to break the symmetry is removed. The right amount of gauge bosons and fermions is needed in balance to stabilize SSB. Upper bounds for fermion and Higgs masses arise naturally.