The Fierz-Pauli theory on curved spacetime at one-loop and its counterterms
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| Format: | Preprint |
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2025
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| _version_ | 1866913736103559168 |
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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 |
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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 |