Ambient space and integration of the trace anomaly
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909428043743232 |
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| author | Paci, Gregorio Zanusso, Omar |
| author_facet | Paci, Gregorio Zanusso, Omar |
| contents | We use the ambient space construction, in which spacetime is mapped into a special lightcone of a higher dimensional manifold, to derive the integrable terms of the trace anomaly in even dimensions. We argue that the natural topological anomaly is the so-called $Q$-curvature, which, when projected from the ambient space, always comes with a Weyl covariant operator that can naturally be adopted for the integration of the anomaly itself in the form of a nonlocal action. The use of the ambient space makes trasparent the fact that there are some new ambiguities in the integration of the anomaly, which we now understand geometrically from the ambient point of view. These ambiguities, which manifest themselves as undetermined parameters in the integrated nonlocal action, become more severe in dimensions $d\geq 6$ and do not seem to be related to a choice of the renormalization scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ambient space and integration of the trace anomaly Paci, Gregorio Zanusso, Omar High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology Mathematical Physics We use the ambient space construction, in which spacetime is mapped into a special lightcone of a higher dimensional manifold, to derive the integrable terms of the trace anomaly in even dimensions. We argue that the natural topological anomaly is the so-called $Q$-curvature, which, when projected from the ambient space, always comes with a Weyl covariant operator that can naturally be adopted for the integration of the anomaly itself in the form of a nonlocal action. The use of the ambient space makes trasparent the fact that there are some new ambiguities in the integration of the anomaly, which we now understand geometrically from the ambient point of view. These ambiguities, which manifest themselves as undetermined parameters in the integrated nonlocal action, become more severe in dimensions $d\geq 6$ and do not seem to be related to a choice of the renormalization scheme. |
| title | Ambient space and integration of the trace anomaly |
| topic | High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2411.03842 |