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

TL;DR

The paper demonstrates that a minimal Generalized Uncertainty Principle (GUP) deformation of the spin-2 Fierz-Pauli action naturally generates a higher-derivative operator equivalent, at quadratic order, to the spin-2 sector of Stelle's curvature-squared gravity, including a Lee-Wick partner for the would-be ghost. Using an auxiliary-field formulation, the higher-derivative structure is diagonalized into a healthy massless spin-2 mode and a LW partner with mass $M$, whose contributions can be rendered nonpropagating via LW contour or PT-symmetric inner products, preserving unitarity. The authors further show that the same GUP deformation is compatible with the Galileon structure of the dRGT helicity-0 sector, with $O(\alpha)$ corrections reducing to total derivatives and leaving the BD ghost absent in the decoupling limit. Overall, the work unifies GUP, LW quantization, and curvature-squared gravity into a framework where Planck-scale physics induces IR modifications without introducing physical ghosts, offering a potential blueprint for ghost-free UV completions of massive gravity. The results hint at a principle in which UV algebraic deformations, rather than solely Lagrangian terms, encode the emergence of infrared gravitational physics and may guide future studies of higher-order corrections and observational consequences.

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.