Effective potentials for de Sitter and anti de Sitter quantum fields
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917306121060352 |
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| author | Bonanno, Alfio Cacciatori, Sergio Luigi Moschella, Ugo |
| author_facet | Bonanno, Alfio Cacciatori, Sergio Luigi Moschella, Ugo |
| contents | We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter backgrounds. We then compute the effective potential for a scalar $O(N)$ theory on a de Sitter space in any integer dimension. In $d=3$ and dimensional regularization, we extend the calculation up to two loops and compute the $β$-function and the anomalous mass dimension. They coincide exactly with flat-space results, despite dramatic curvature modifications to physical masses/couplings. The flat limit $R\to\infty$ recovers Coleman-Weinberg, confirming consistency. Working in $d=3$ dimensions, we repeat the calculation for $AdS_3$ by using point-splitting regularization, obtaining analogous results for the $β$-function and anomalous mass dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective potentials for de Sitter and anti de Sitter quantum fields Bonanno, Alfio Cacciatori, Sergio Luigi Moschella, Ugo High Energy Physics - Theory General Relativity and Quantum Cosmology We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter backgrounds. We then compute the effective potential for a scalar $O(N)$ theory on a de Sitter space in any integer dimension. In $d=3$ and dimensional regularization, we extend the calculation up to two loops and compute the $β$-function and the anomalous mass dimension. They coincide exactly with flat-space results, despite dramatic curvature modifications to physical masses/couplings. The flat limit $R\to\infty$ recovers Coleman-Weinberg, confirming consistency. Working in $d=3$ dimensions, we repeat the calculation for $AdS_3$ by using point-splitting regularization, obtaining analogous results for the $β$-function and anomalous mass dimension. |
| title | Effective potentials for de Sitter and anti de Sitter quantum fields |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.02140 |