Lorentz Symmetry Violation in QCD and the Frustration of Asymptotic Freedom

TL;DR

This paper investigates how Lorentz symmetry violation affects the high-energy behavior of QCD, revealing that such violation can prevent asymptotic freedom and cause the coupling to increase at very high energies.

Contribution

It explores the impact of Lorentz symmetry violation on the renormalization group flow in QCD, showing that asymptotic freedom can be frustrated by certain LSV scenarios.

Findings

Asymptotic freedom is hindered by Lorentz symmetry violation.

The running coupling reaches a minimum and then increases at high energies.

The LSV parameter grows without bound at high energy.

Abstract

We study the effect of Lorentz symmetry violation (LSV) on the behaviour at high energy of SU(N) gauge theory with quarks in the fundamental representation. The approach is similar to that for QED treated in a previous paper. In contrast to QED, standard Lorentz invariant QCD is asymptotically free. Our aim is to explore the structure of the renormalisation group at high energy and hence weak coupling without requiring the Lorentz symmetry breaking to be small. The simplest type of LSV leaves the theory invariant under a subgroup of the Lorentz group that preserves a (time-like) 4-vector. We examine this case in detail and find that asymptotic freedom is frustrated. That is, at sufficiently high energy the running coupling constant attains a minimum value before increasing again, while the LSV parameter increases without bound.