Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory

TL;DR

This paper demonstrates that Lorentz symmetry, broken at high energies in a Lifshitz-type scalar theory, is dynamically restored at low energies using nonperturbative renormalization group methods, ensuring ultraviolet completeness.

Contribution

It shows the Lorentz symmetry restoration in Lifshitz-type scalar theories via exact renormalization group analysis, establishing their ultraviolet completeness and allowing nontrivial interactions.

Findings

Broken symmetry terms vanish in the infrared

Lorentz symmetry is dynamically restored at low energy

Theories remain renormalizable with nontrivial interactions

Abstract

The purpose of this paper is to present our study on the restoration of the Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by using nonperturbative methods. We apply the Wegner-Houghton equation, which is one of the exact renormalization group equations, to the Lifshitz-type theory. Analyzing the equation for a z=2, d=3+1 Lifshitz-type scalar model, and using some variable transformations, we found that broken symmetry terms vanish in the infrared region. This shows that the Lifshitz-type scalar model dynamically restores the Lorentz symmetry at low energy. Our result provides a definition of ultraviolet complete renormalizable scalar field theories. These theories can have nontrivial interaction terms of \phi^{n} (n=4, 6, 8, 10) even when the Lorentz symmetry is restored at low energy.