Spin-2 fields, Lee-Wick Ghosts, and GUP

TL;DR

This paper explores how a minimal Generalized Uncertainty Principle (GUP) deformation influences higher-derivative spin-2 theories, linking them to Lee-Wick ghosts and curvature-squared gravity, while maintaining ghost-free properties.

Contribution

It demonstrates that GUP deformations induce higher-derivative terms equivalent to curvature-squared gravity and can be reformulated as Lee-Wick partners, unifying these concepts within a consistent framework.

Findings

GUP deformation leads to higher-derivative spin-2 actions similar to Stelle's gravity.

The higher-derivative terms can be recast as Lee-Wick partners, avoiding propagating ghosts.

GUP corrections preserve the ghost-free structure of massive gravity models.

Abstract

We revisit the structure of higher-derivative spin-2 theories from the perspective of the Generalized Uncertainty Principle (GUP). We show that a minimal GUP deformation of the Fierz-Pauli (FP) action induces a higher-derivative kinetic operator equivalent, at quadratic order, to the spin-2 sector of Stelle's curvature-squared gravity. Via an auxiliary-field formulation, the GUP-generated higher derivative can be recast as a Lee-Wick (LW) partner of the spin-2. We then demonstrate that the same GUP deformation is compatible with the Galileon structure governing the helicity-0 mode in dRGT massive gravity. The GUP corrections reduce to total derivatives, preserving the absence of the Boulware-Deser ghost. Our results unify GUP models, LW quantization, and curvature-squared gravity into a single framework, in which the higher-derivative spin-2 ghost is rendered non-propagating while the nonlinear massive completion remains intact.