Gubser, Steven S. and Heydeman, Matthew and Jepsen, Christian and Marcolli, Matilde and Parikh, Sarthak and Saberi, Ingmar and Stoica, Bogdan and Trundy, Brian (2017) Edge length dynamics on graphs with applications to p-adic AdS/CFT. Journal of High Energy Physics, 2017 (6). pp. 1-35. ISSN 1029-8479. doi:10.1007/JHEP06(2017)157. https://resolver.caltech.edu/CaltechAUTHORS:20170707-065452085
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Abstract
We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles should be sufficiently long. The infinite regular tree with all edge lengths equal is an example of a graph with constant negative curvature, providing a connection with p-adic AdS/CFT, where such a tree takes the place of anti-de Sitter space. We compute simple correlators of the operator holographically dual to edge length fluctuations. This operator has dimension equal to the dimension of the boundary, and it has some features in common with the stress tensor.
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| Additional Information: | © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: May 18, 2017. Accepted: June 18, 2017. Published: June 30, 2017. Article funded by SCOAP3. The work of S. Gubser, C. Jepsen, S. Parikh, and B. Trundy was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671. The work of M. Heydeman was supported by the Department of Energy under grant DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech. M. Marcolli is partially supported by NSF grants DMS-1201512 and PHY-1205440, and by the Perimeter Institute for Theoretical Physics. The work of B. Stoica was supported in part by the Simons Foundation, and by the U.S. Department of Energy under grant DE-SC-0009987. | ||||||||||||||||||||
| Group: | Walter Burke Institute for Theoretical Physics | ||||||||||||||||||||
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| Subject Keywords: | Lattice Models of Gravity; AdS-CFT Correspondence; Classical Theories of Gravity | ||||||||||||||||||||
| Issue or Number: | 6 | ||||||||||||||||||||
| DOI: | 10.1007/JHEP06(2017)157 | ||||||||||||||||||||
| Record Number: | CaltechAUTHORS:20170707-065452085 | ||||||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170707-065452085 | ||||||||||||||||||||
| Official Citation: | Gubser, S.S., Heydeman, M., Jepsen, C. et al. J. High Energ. Phys. (2017) 2017: 1. doi:10.1007/JHEP06(2017)157 | ||||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||||
| ID Code: | 78825 | ||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||||||||||
| Deposited On: | 07 Jul 2017 17:31 | ||||||||||||||||||||
| Last Modified: | 15 Nov 2021 17:43 |
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