Nonpolynomial Normal Modes of the Renormalization Group in the Presence of a Constant Vector Potential Background

TL;DR

This paper investigates how a constant vector potential background influences the renormalization group flow, finding that it does not introduce new relevant modes and likely has no physical effects due to gauge invariance.

Contribution

It demonstrates that the presence of a constant vector potential does not generate new nonpolynomial normal modes in the renormalization group flow for scalar and fermionic theories.

Findings

Vector potential modifies scalar field renormalization only.

No evidence of relevant modes in fermionic theories.

Results support gauge invariance and physical irrelevance of the vector potential.

Abstract

We examine the renormalization group flow in the vicinity of the free-field fixed point for effective field theories in the presence of a constant, nondynamical vector potential background. The interaction with this vector potential represents the simplest possible form of Lorentz violation. We search for any normal modes of the flow involving nonpolynomial interactions. For scalar fields, the inclusion of the vector potential modifies the known modes only through a change in the field strength renormalization. For fermionic theories, where an infinite number of particle species are required in order for nonpolynomial interactions to be possible, we find no evidence for any analogous relevant modes. These results are consistent with the idea that the vector potential interaction, which may be eliminated from the action by a gauge transformation, should have no physical effects.