Effects of Spontaneous Lorentz Violation in Gravity

TL;DR

This paper investigates the theoretical implications of spontaneous Lorentz symmetry breaking in gravity, exploring associated phenomena like Nambu-Goldstone modes, the Higgs mechanism, and their effects in different spacetime geometries.

Contribution

It provides a detailed analysis of Lorentz violation effects in gravity, including the possibility of a Higgs mechanism in Riemann-Cartan spacetime and the emergence of massive modes in a bumblebee model.

Findings

Conventional Higgs mechanism does not occur in Riemann spacetime.

A Higgs mechanism involving the spin connection is possible in Riemann-Cartan spacetime.

Unconventional massive modes can appear in the metric through non-standard processes.

Abstract

Spontaneous breaking of local Lorentz symmetry occurs when a local vector or tensor field acquires a nonzero vacuum expectation value. The effects of such breaking are examined in the context of gravity theory. These include an associated spontaneous breaking of diffeomorphism symmetry and generation of massless Nambu-Goldstone modes. The possibility of a Higgs mechanism is examined as well, and it is found that the conventional Higgs mechanism (giving rise to massive gauge fields) does not occur in a Riemann spacetime. However, in a Riemann-Cartan spacetime a Higgs mechanism involving the spin connection is possible. Despite the lack of a conventional Higgs mechanism in Riemann spacetime, additional massive modes involving the metric can appear through unconventional processes that have no analogue in nonabelian gauge theory. The effects of these types of processes are illustrated using a specific model, known as a bumblebee model, in which a vector field acquires a vacuum value.