Time Geometrization of Manifold C; Time-Structured Holographic Duality: A Mapping Theory between Boundary Temporal Fiber Bundles and Bulk Spacetime Topology
Fuente:
Zenodo
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Recurso digital |
| Publié: |
Zenodo
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901592419074048 |
|---|---|
| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>This paper proposes and develops a theoretical framework named “Time-Structured<br>Holographic Duality,” which systematically extends the traditional AdS/CFT cor<br>respondence principle. Within this framework, the intrinsic geometric and topo<br>logical structure of the time dimension in the boundary conformal field theory—<br>specifically described by the “temporal fiber bundle” and its associated connection,<br>curvature, and cohomology groups—is established as the mapping source for the<br>causal and topological structure of the dual bulk gravitational spacetime. We<br>construct an extended holographic dictionary, mapping the boundary’s temporal<br>curvature and the dimension of the first-order temporal cohomology group to the<br>tidal force’s temporal components and the Cauchy horizon stability in the bulk<br>spacetime, respectively. Using the three-dimensional N = 6 ABJM theory and its<br>dual AdS4 × S7/Zk spacetime as a concrete example, we design numerical exper<br>iments combining lattice field theory and discrete geometry. The results indicate<br>an empirical correlation between the dynamical features of the boundary renormal<br>ization group flow near fixed points (such as the minimal eigenvalue λmin of the<br>linearized operator) and topological invariants of the bulk spacetime. This corre<br>lation is confirmed for statistical significance (p < 0.01) via bootstrap tests. Based<br>on this framework, we derive a universal topological lower bound theorem concern<br>ing the mass gap of the boundary theory, and propose a new interpretation of the<br>black hole information paradox recovery time based on the dimension of temporal<br>cohomology. This provides a new, computable perspective on the emergence of<br>causal structure and information issues in quantum gravity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18093462 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Time Geometrization of Manifold C; Time-Structured Holographic Duality: A Mapping Theory between Boundary Temporal Fiber Bundles and Bulk Spacetime Topology zhou, changzheng zhou, ziqing Holographic Duality; Time-Structured; Temporal Cohomology; Topological Gravity; ABJM Theory; Black Hole Information Problem; Numerical Quantum Gravity <p>This paper proposes and develops a theoretical framework named “Time-Structured<br>Holographic Duality,” which systematically extends the traditional AdS/CFT cor<br>respondence principle. Within this framework, the intrinsic geometric and topo<br>logical structure of the time dimension in the boundary conformal field theory—<br>specifically described by the “temporal fiber bundle” and its associated connection,<br>curvature, and cohomology groups—is established as the mapping source for the<br>causal and topological structure of the dual bulk gravitational spacetime. We<br>construct an extended holographic dictionary, mapping the boundary’s temporal<br>curvature and the dimension of the first-order temporal cohomology group to the<br>tidal force’s temporal components and the Cauchy horizon stability in the bulk<br>spacetime, respectively. Using the three-dimensional N = 6 ABJM theory and its<br>dual AdS4 × S7/Zk spacetime as a concrete example, we design numerical exper<br>iments combining lattice field theory and discrete geometry. The results indicate<br>an empirical correlation between the dynamical features of the boundary renormal<br>ization group flow near fixed points (such as the minimal eigenvalue λmin of the<br>linearized operator) and topological invariants of the bulk spacetime. This corre<br>lation is confirmed for statistical significance (p < 0.01) via bootstrap tests. Based<br>on this framework, we derive a universal topological lower bound theorem concern<br>ing the mass gap of the boundary theory, and propose a new interpretation of the<br>black hole information paradox recovery time based on the dimension of temporal<br>cohomology. This provides a new, computable perspective on the emergence of<br>causal structure and information issues in quantum gravity.</p> |
| title | Time Geometrization of Manifold C; Time-Structured Holographic Duality: A Mapping Theory between Boundary Temporal Fiber Bundles and Bulk Spacetime Topology |
| topic | Holographic Duality; Time-Structured; Temporal Cohomology; Topological Gravity; ABJM Theory; Black Hole Information Problem; Numerical Quantum Gravity |
| url | https://doi.org/10.5281/zenodo.18093462 |