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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.19315 |
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| _version_ | 1866908743142211584 |
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| author | Silva, Agustín |
| author_facet | Silva, Agustín |
| contents | We explore a new route toward a non-perturbative quantization of gravity based on a purely affine formulation, where the affine connection is the fundamental field and the metric, when it exists, emerges as a derived quantity. Starting from the Palatini formulation of General Relativity, we recall how an equivalent Eddington-type purely affine action arises at the classical level under mild assumptions. A key feature for the non-perturbative program is that, in the pure gravity case, for a positive cosmological constant, the action is bounded below, allowing one to define a well-posed statistical ensemble of connections. We discretize this theory on a fixed hypercubic lattice and construct the corresponding partition function, including torsionful and torsionless ensembles. We provide an open C++ Monte Carlo implementation that can simulate these ensembles in arbitrary dimension, and we present proof-of-principle results in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A pathway to non-perturbative Quantum Affine Gravity Silva, Agustín High Energy Physics - Theory General Relativity and Quantum Cosmology We explore a new route toward a non-perturbative quantization of gravity based on a purely affine formulation, where the affine connection is the fundamental field and the metric, when it exists, emerges as a derived quantity. Starting from the Palatini formulation of General Relativity, we recall how an equivalent Eddington-type purely affine action arises at the classical level under mild assumptions. A key feature for the non-perturbative program is that, in the pure gravity case, for a positive cosmological constant, the action is bounded below, allowing one to define a well-posed statistical ensemble of connections. We discretize this theory on a fixed hypercubic lattice and construct the corresponding partition function, including torsionful and torsionless ensembles. We provide an open C++ Monte Carlo implementation that can simulate these ensembles in arbitrary dimension, and we present proof-of-principle results in two dimensions. |
| title | A pathway to non-perturbative Quantum Affine Gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.19315 |