$CP^{(N-1)}$ model in aether-superspace

TL;DR

This paper investigates how Lorentz-violating backgrounds influence mass generation in the $CP^{(N-1)}$ model within aether-superspace, revealing dependence on background properties except for spacelike LV vectors.

Contribution

It demonstrates that in aether-superspace, the dynamical mass generation in the $CP^{(N-1)}$ model depends on Lorentz-violating parameters, unlike the Lorentz-invariant case.

Findings

Mass depends on Lorentz-violating background properties.

Spacelike LV vector parameter does not affect mass.

Contrast with QED where mass depends on all LV parameters.

Abstract

In this paper we study the dynamical generation of mass in the Lorentz-violating $CP^{(N-1)}$ model defined in two and three-dimensional aether-superspace. We show that even though the model presents a phase structure similar to the usual, Lorentz invariant case, the dynamically generated mass by quantum corrections has a dependence on the Lorentz violating background properties, except for spacelike LV vector parameter. This is to be contrasted with the behavior of the quantum electrodynamics in the two-dimensional aether-superspace, where the dynamical generation of mass was shown to exhibit an explicit dependence on the aether parameters in every possible case.