On the Cut-off Estimate in Lifshitz Five Dimensional Field Theories

TL;DR

This paper investigates whether Lifshitz-type higher dimensional operators can improve the high-energy behavior of five-dimensional gauge theories, finding improvements in transverse modes but issues with longitudinal modes in non-abelian cases.

Contribution

It demonstrates that Lifshitz operators can enhance UV behavior of 5D gauge theories' transverse modes but do not improve longitudinal modes in non-abelian theories, highlighting the special nature of standard 5D models.

Findings

UV behavior of transverse gauge modes is improved by Lifshitz operators.

Longitudinal modes become strongly coupled at lower energies.

Improvement is linked to locality, gauge symmetries, and lowest dimensional operators.

Abstract

We analyze if and to what extent the high energy behaviour of five-dimensional (5D) gauge theories can be improved by adding certain higher dimensional operators of "Lifshitz" type, without breaking the ordinary four-dimensional Lorentz symmetries. We show that the UV behaviour of the transverse gauge field polarizations can be improved by the Lifshitz operators, while the longitudinal polarizations get strongly coupled at energies lower than the ones in ordinary 5D theories, spoiling the usefulness of the construction in non-abelian gauge theories. We conclude that the improved behaviour as effective theories of the ordinary 5D models is not only related to locality and 5D gauge symmetries, but is a special property of the standard theories defined by the lowest dimensional operators.