Computing renormalized curvature integrals on Poincaré-Einstein manifolds
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917421037649920 |
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| author | Case, Jeffrey S. Khaitan, Ayush Lin, Yueh-Ju Tyrrell, Aaron J. Yuan, Wei |
| author_facet | Case, Jeffrey S. Khaitan, Ayush Lin, Yueh-Ju Tyrrell, Aaron J. Yuan, Wei |
| contents | We describe a general procedure for computing renormalized curvature integrals on Poincaré-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-type formulas of Albin and Chang-Qing-Yang for the renormalized volume, and explicitly identify a scalar conformal invariant in the latter formula. Our approach constructs scalar conformal invariants of weight $-n$ on $n$-manifolds, $n \geq 8$, that are natural divergences; these imply that the scalar invariant in the Chang-Qing-Yang formula is not unique in dimension $n \geq 8$. Our procedure also produces explicit conformally invariant Gauss--Bonnet-type formulas for compact Einstein manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing renormalized curvature integrals on Poincaré-Einstein manifolds Case, Jeffrey S. Khaitan, Ayush Lin, Yueh-Ju Tyrrell, Aaron J. Yuan, Wei Differential Geometry High Energy Physics - Theory We describe a general procedure for computing renormalized curvature integrals on Poincaré-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-type formulas of Albin and Chang-Qing-Yang for the renormalized volume, and explicitly identify a scalar conformal invariant in the latter formula. Our approach constructs scalar conformal invariants of weight $-n$ on $n$-manifolds, $n \geq 8$, that are natural divergences; these imply that the scalar invariant in the Chang-Qing-Yang formula is not unique in dimension $n \geq 8$. Our procedure also produces explicit conformally invariant Gauss--Bonnet-type formulas for compact Einstein manifolds. |
| title | Computing renormalized curvature integrals on Poincaré-Einstein manifolds |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.11319 |