Duality Anomalies in Linearized Gravity
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918131064111104 |
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| author | Borsten, Leron Duff, Michael J. Kanakaris, Dimitri Kim, Hyungrok |
| author_facet | Borsten, Leron Duff, Michael J. Kanakaris, Dimitri Kim, Hyungrok |
| contents | Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. Proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be quantum inequivalent in even dimensions. The duality anomaly is obtained by resolving the dual graviton theories into vector-valued $p$-form electrodynamics and is controlled by the Reidemeister torsion, Ray-Singer torsion and Euler characteristic of the cotangent bundle. Under the proposed instanton prescription the duality anomaly vanishes for an odd number of spacetime dimensions as a consequence of the celebrated Cheeger-Müller theorem. In the presence of a gravitational $θ$-term, the partition function is a modular form in direct analogy to Abelian S-duality for Maxwell theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Duality Anomalies in Linearized Gravity Borsten, Leron Duff, Michael J. Kanakaris, Dimitri Kim, Hyungrok High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 81T50 (Primary) 83C25, 58J52, 57Q10 (Secondary) Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. Proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be quantum inequivalent in even dimensions. The duality anomaly is obtained by resolving the dual graviton theories into vector-valued $p$-form electrodynamics and is controlled by the Reidemeister torsion, Ray-Singer torsion and Euler characteristic of the cotangent bundle. Under the proposed instanton prescription the duality anomaly vanishes for an odd number of spacetime dimensions as a consequence of the celebrated Cheeger-Müller theorem. In the presence of a gravitational $θ$-term, the partition function is a modular form in direct analogy to Abelian S-duality for Maxwell theory. |
| title | Duality Anomalies in Linearized Gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 81T50 (Primary) 83C25, 58J52, 57Q10 (Secondary) |
| url | https://arxiv.org/abs/2504.15973 |