The Higgs mechanism in Finsler spacetimes

TL;DR

This paper explores how Finsler geometry, which extends Riemannian geometry, affects gauge field theories with spontaneous symmetry breaking, highlighting modified dispersion relations and Lorentz violation implications.

Contribution

It investigates the impact of Finsler spacetime structures on the Higgs mechanism and gauge theories, including Lorentz violation and SSB in mono-metric Finsler models.

Findings

Modified dispersion relations arise in Finsler backgrounds.

Lorentz violating operators can percolate to lower dimensions.

SSB can be consistent within Finsler spacetime frameworks.

Abstract

Finsler geometry has been recently re-discovered as an interesting possibility to describe spacetime geometry beyond Riemannian geometry. The most evident effect of this class of models is the prediction of modified dispersion relations for particles moving in such backgrounds. In this paper, we are going to consider the effects of modified dispersion relations on a gauge field theory with spontaneous symmetry breaking (SSB) associated to a Higgs field. The percolation of higher dimensional, Lorentz violating operators to lower dimensional ones is discussed. We also discuss the issue of SSB in a mono-metric Finsler scenario like the one associated to the so-called very special relativity.