The Fierz-Pauli theory on curved spacetime at one-loop and its counterterms

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Main Authors: Farolfi, Leonardo, Fecit, Filippo
Format: Preprint
Published: 2025
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author Farolfi, Leonardo
Fecit, Filippo
author_facet Farolfi, Leonardo
Fecit, Filippo
contents We compute the first four heat-kernel coefficients required for the renormalization of Linearized Massive Gravity. We focus on the Fierz-Pauli theory in a curved spacetime, describing the propagation of a massive spin $2$ field in a non-flat background. The background must be on-shell, i.e. must be an Einstein space, in order to ensure a consistent extension of the Fierz-Pauli theory beyond Minkowski space. Starting from the Stückelberg formulation with restored gauge invariance, we apply suitable gauge-fixing procedures to simplify the complicated non-minimal kinetic operators of the scalar, vector, and tensor sectors of the theory, reducing them into manageable minimal forms. Using standard techniques, we then compute the Seeley-DeWitt coefficients, with particular emphasis on the fourth coefficient, $a_3(D)$, in arbitrary spacetime dimensions. This result constitutes our main contribution, as it has not been previously reported in full generality in the literature.
format Preprint
id arxiv_https___arxiv_org_abs_2503_11304
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Fierz-Pauli theory on curved spacetime at one-loop and its counterterms
Farolfi, Leonardo
Fecit, Filippo
High Energy Physics - Theory
We compute the first four heat-kernel coefficients required for the renormalization of Linearized Massive Gravity. We focus on the Fierz-Pauli theory in a curved spacetime, describing the propagation of a massive spin $2$ field in a non-flat background. The background must be on-shell, i.e. must be an Einstein space, in order to ensure a consistent extension of the Fierz-Pauli theory beyond Minkowski space. Starting from the Stückelberg formulation with restored gauge invariance, we apply suitable gauge-fixing procedures to simplify the complicated non-minimal kinetic operators of the scalar, vector, and tensor sectors of the theory, reducing them into manageable minimal forms. Using standard techniques, we then compute the Seeley-DeWitt coefficients, with particular emphasis on the fourth coefficient, $a_3(D)$, in arbitrary spacetime dimensions. This result constitutes our main contribution, as it has not been previously reported in full generality in the literature.
title The Fierz-Pauli theory on curved spacetime at one-loop and its counterterms
topic High Energy Physics - Theory
url https://arxiv.org/abs/2503.11304