Liouville-Lifshitz theory in 3+1 dimensions

TL;DR

This paper analyzes a four-dimensional z=3 Lifshitz theory with Liouville potential, deriving its exact renormalized potential, non-perturbative coupling relations, and demonstrating emergent Lorentz symmetry in the infrared, with implications for high-energy physics.

Contribution

It provides the exact renormalized potential and non-perturbative coupling relations for a 4D Lifshitz Liouville theory and shows Lorentz symmetry emerges quantum mechanically.

Findings

Exact renormalized potential derived

Non-perturbative relation between couplings established

Lorentz symmetry emerges in the infrared regime

Abstract

We consider a four-dimensional theory in the z=3 Lifshitz context, with an exponential (Liouville) potential. We determine the exact renormalized potential of the theory and derive the non-perturbative relation between the renormalized and bare couplings. In addition, we show that Lorentz symmetry is naturally generated by quantum fluctuations in the infrared regime, and conclude that the model can be relevant to High Energy Physics.