No Lee-Wick Fields out of Gravity

TL;DR

This paper analyzes gravitational one-loop divergences in the standard model with large extra dimensions, showing that Lee-Wick higher derivative terms do not correspond to ghost fields, challenging previous claims about their existence.

Contribution

The study clarifies the relationship between higher derivative counterterms and Lee-Wick ghost fields, providing a detailed regularization approach in extra-dimensional gravity models.

Findings

Fermionic and scalar counterterms differ from Lee-Wick higher derivative terms.

Lee-Wick higher derivative terms do not imply the existence of ghost fields.

Regularization method preserves gauge invariance in divergence calculations.

Abstract

We investigate the gravitational one-loop divergences of the standard model in large extra dimensions, with gravitons propagating in the (4+delta)-dimensional bulk and gauge fields as well as scalar and fermionic multiplets confined to a three-brane. To determine the divergences we establish a cut-off regularization which allows us to extract gauge-invariant counterterms. In contrast to the claim of a recent paper [arXiv:0807.0132], we show that the fermionic and scalar higher derivative counterterms do not coincide with the higher derivative terms in the Lee-Wick standard model. We argue that even if the exact Lee-Wick higher derivative terms were found, as in the case of the pure gauge sector, this would not allow to conclude the existence of the massive ghost fields corresponding to these higher derivative terms in the Lee-Wick standard model.