Field Theory at a Lifshitz Point

TL;DR

This paper develops renormalizable scalar and gauge field theories at a Lifshitz point with broken Lorentz invariance in the UV, exploring their implications for dispersion relations, cosmology, and gamma-ray burst observations.

Contribution

It constructs the general form of renormalizable actions at a Lifshitz point and analyzes their physical implications, including modified dispersion relations and cosmological effects.

Findings

Lorentz invariance is recovered in the IR limit.

Modified dispersion relations explain gamma-ray burst time delays.

Theories are UV complete with broken Lorentz symmetry.

Abstract

We construct the general renormalizable actions for the scalar field and the gauge field at a Lifshitz point characterized by the dynamical critical exponent $z$. The Lorentz invariance is broken down in the UV region, but is recovered in the IR limit. Even though the theories are UV complete, the speed of light is related to the momentum by $z(k/M)^{z-1}$ which can go to infinity in the UV limit for $z\geq 2$. Since the Lorentz invariance is broken down, the dispersion relation is modified and the time delays in Gamma-Ray bursts can be easily explained. In addition, we also discuss the thermal dynamics and the size of causal patch in a FRW universe for the field theory at a Lifshitz point.