Regulator Dependence of the Proposed UV Completion of the Ghost Condensate

TL;DR

This paper investigates whether a proposed UV completion of ghost condensate theories is regulator-dependent, finding that using a non-perturbative lattice regulator prevents ghost condensate formation, thus questioning its universality.

Contribution

It demonstrates that the formation of ghost condensates in this theory depends on the choice of regulator, challenging previous claims of a regulator-independent UV completion.

Findings

Lattice regulator prevents ghost condensate formation.

Regulator choice affects the theory's IR properties.

UV completion is regulator dependent.

Abstract

Recently, it was shown that a renormalizable theory of heavy fermions coupled to a light complex boson could generate an effective action for the boson with the properties required to violate Lorentz invariance spontaneously through the mechanism of ghost condensation. However, there was some doubt about whether this result depended on the choice of regulator. In this work, we adopt a non-perturbative, unitary lattice regulator and show that with this regulator the theory does not have the properties necessary to form a ghost condensate. Consequently, the statement that the theory is a UV completion of the Higgs phase of gravity is regulator dependent.