On Emergent Gauge and Gravity Theories

TL;DR

This paper explores how gauge and gravity theories can emerge from spontaneous Lorentz invariance violation in tensor fields, leading to a framework resembling linearized general relativity with additional Lorentz-violating couplings.

Contribution

It demonstrates that linearized gravity can emerge from a symmetric tensor field theory with SLIV constraints, linking emergent gauge invariance to spontaneous Lorentz violation.

Findings

Emergent tensor field gravity corresponds to linearized general relativity.

Goldstone modes from SLIV form the physical graviton.

Lorentz-violating couplings do not produce observable violations in extended theories.

Abstract

We present some general approach to emergent gauge theories and consider in significant detail the emergent tensor field gravity case. In essence, an arbitrary local theory of a symmetric two-tensor field $H_{\mu \nu}$ in Minkowski spacetime is considered, in which the equations of motion are required to be compatible with a nonlinear $\sigma $ model type length-fixing constraint $H_{\mu \nu}^{2}=\pm M^{2}$ leading to spontaneous Lorentz invariance violation, SLIV ($M$ is the proposed scale for SLIV). Allowing the parameters in the Lagrangian to be adjusted so as to be consistent with this constraint, the theory turns out to correspond to linearized general relativity in the weak field approximation, while some of the massless tensor Goldstone modes appearing through SLIV are naturally collected in the physical graviton. The underlying diffeomophism invariance emerges as a necessary condition for the tensor field $H_{\mu \nu}$ not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in the theory is chosen by SLIV. The emergent theory appears essentially nonlinear, when expressed in terms of the pure Goldstone tensor modes and contains a plethora of new Lorentz and $CPT$ violating couplings. However, these couplings do not lead to physical Lorentz violation once this tensor field gravity is properly extended to conventional general relativity.