Wormhole Renormalization: The gravitational path integral, holography, and a gauge group for topology change
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| Format: | Preprint |
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2024
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| _version_ | 1866913451538907136 |
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| author | Gesteau, Elliott Marcolli, Matilde McNamara, Jacob |
| author_facet | Gesteau, Elliott Marcolli, Matilde McNamara, Jacob |
| contents | We study the Factorization Paradox from the bottom up by adapting methods from perturbative renormalization. Just as quantum field theories are plagued with loop divergences that need to be cancelled systematically by introducing counterterms, gravitational path integrals are plagued by wormhole contributions that spoil the factorization of the holographic dual. These wormholes must be cancelled by some stringy effects in a UV complete, holographic theory of quantum gravity. In a simple model of two-dimensional topological gravity, we outline a gravitational analog of the recursive BPHZ procedure in order to systematically introduce ``counter-wormholes" which parametrize the unknown stringy effects that lead to factorization. Underlying this procedure is a Hopf algebra of symmetries which is analogous to the Connes--Kreimer Hopf algebra underlying perturbative renormalization. The group dual to this Hopf algebra acts to reorganize contributions from spacetimes with distinct topology, and can be seen as a gauge group relating various equivalent ways of constructing a factorizing gravitational path integral. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_20324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wormhole Renormalization: The gravitational path integral, holography, and a gauge group for topology change Gesteau, Elliott Marcolli, Matilde McNamara, Jacob High Energy Physics - Theory Mathematical Physics Combinatorics Quantum Algebra We study the Factorization Paradox from the bottom up by adapting methods from perturbative renormalization. Just as quantum field theories are plagued with loop divergences that need to be cancelled systematically by introducing counterterms, gravitational path integrals are plagued by wormhole contributions that spoil the factorization of the holographic dual. These wormholes must be cancelled by some stringy effects in a UV complete, holographic theory of quantum gravity. In a simple model of two-dimensional topological gravity, we outline a gravitational analog of the recursive BPHZ procedure in order to systematically introduce ``counter-wormholes" which parametrize the unknown stringy effects that lead to factorization. Underlying this procedure is a Hopf algebra of symmetries which is analogous to the Connes--Kreimer Hopf algebra underlying perturbative renormalization. The group dual to this Hopf algebra acts to reorganize contributions from spacetimes with distinct topology, and can be seen as a gauge group relating various equivalent ways of constructing a factorizing gravitational path integral. |
| title | Wormhole Renormalization: The gravitational path integral, holography, and a gauge group for topology change |
| topic | High Energy Physics - Theory Mathematical Physics Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2407.20324 |