[Paper Review] Effects of Spontaneous Lorentz Violation in Gravity

Robert Bluhm|ArXiv.org|Dec 30, 2007

Noncommutative and Quantum Gravity Theories2 references3 citations

TL;DR

This paper investigates spontaneous Lorentz violation in gravity using a bumblebee model with a vector field acquiring a vacuum expectation value. It shows that while a conventional Higgs mechanism for diffeomorphisms fails in Riemann spacetime, massive modes can still emerge via unconventional metric interactions, altering gravitational potentials, and that Nambu-Goldstone modes can propagate like photons in certain gauges.

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.

Motivation & Objective

• To analyze the consequences of spontaneous local Lorentz symmetry breaking in gravitational theories.
• To determine whether a Higgs mechanism can occur in Riemann versus Riemann-Cartan spacetime when Lorentz symmetry is spontaneously broken.
• To investigate the nature and detectability of Nambu-Goldstone and massive modes arising from such symmetry breaking.
• To connect the resulting low-energy phenomenology to the Standard-Model Extension (SME), particularly in the context of gravitational and matter field couplings.

Proposed method

• Uses a vierbein formalism to describe local Lorentz and diffeomorphism symmetries in curved spacetime.
• Applies the bumblebee model—a vector field with a non-zero vacuum expectation value—to study spontaneous Lorentz violation.
• Analyzes the role of the spin connection in Riemann-Cartan spacetime, where a Higgs mechanism for Lorentz symmetry can occur.
• Examines the propagation of Nambu-Goldstone modes in axial gauge, showing they behave like photons in the KS bumblebee model.
• Considers alternative mechanisms for massive mode generation in Riemann spacetime, distinct from non-Abelian gauge theory.
• Compares results to the SME framework, showing that all low-energy signals of Lorentz violation can be captured within the SME.

Experimental results

Research questions

• RQ1 Can a conventional Higgs mechanism for diffeomorphism symmetry occur when local Lorentz symmetry is spontaneously broken in Riemann spacetime?
• RQ2 Under what conditions can a Higgs mechanism for Lorentz symmetry arise, and how does the spacetime geometry (Riemann vs. Riemann-Cartan) affect this?
• RQ3 What is the nature and physical behavior of the Nambu-Goldstone modes arising from spontaneous Lorentz violation in gravity?
• RQ4 How do additional massive modes—beyond the conventional Higgs mechanism—arise and affect gravitational dynamics?
• RQ5 To what extent can the phenomenology of spontaneous Lorentz violation be described within the Standard-Model Extension (SME) framework?

Key findings

• Up to ten Nambu-Goldstone modes can emerge from spontaneous local Lorentz violation, all of which can be incorporated into the vierbein field.
• In the KS bumblebee model, Lorentz Nambu-Goldstone modes propagate like photons in an axial gauge, indicating potential detectability.
• A conventional Higgs mechanism for diffeomorphisms does not occur in Riemann spacetime, even with spontaneous Lorentz breaking.
• In Riemann-Cartan spacetime, a Higgs mechanism for Lorentz symmetry is possible, where the spin connection acquires mass.
• In Riemann spacetime, alternative mechanisms generate additional massive modes involving the metric field, which can alter the form of the static gravitational potential.
• All low-energy signals of spontaneous Lorentz violation, including those from Nambu-Goldstone and massive modes, are comprehensively described by the SME framework.