Edge length dynamics on graphs with applications to padic AdS/CFT
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 EinsteinHilbert 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 padic AdS/CFT, where such a tree takes the place of antide Sitter space. Here, 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.
 Authors:

^{[1]};
^{[2]};
^{[1]};
^{[3]};
^{[1]};
^{[4]};
^{[5]};
^{[1]}
 Princeton Univ., NJ (United States). Joseph Henry Lab.
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Dept. of Mathematics
 RuprechtKarls Univ. Heidelberg, Heidelberg (Germany). Mathematisches Inst.
 Brandeis Univ., Waltham, MA (United States). Martin A. Fisher School of Physics
 Publication Date:
 Grant/Contract Number:
 FG0291ER40671; SC0011632; DMS1201512; PHY1205440; SC0009987
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Princeton Univ., NJ (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE; National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lattice Models of Gravity; AdSCFT Correspondence; Classical Theories of Gravity
 OSTI Identifier:
 1425489
Gubser, Steven S., Heydeman, Matthew, Jepsen, Christian, Marcolli, Matilde, Parikh, Sarthak, Saberi, Ingmar, Stoica, Bogdan, and Trundy, Brian. Edge length dynamics on graphs with applications to padic AdS/CFT. United States: N. p.,
Web. doi:10.1007/JHEP06(2017)157.
Gubser, Steven S., Heydeman, Matthew, Jepsen, Christian, Marcolli, Matilde, Parikh, Sarthak, Saberi, Ingmar, Stoica, Bogdan, & Trundy, Brian. Edge length dynamics on graphs with applications to padic AdS/CFT. United States. doi:10.1007/JHEP06(2017)157.
Gubser, Steven S., Heydeman, Matthew, Jepsen, Christian, Marcolli, Matilde, Parikh, Sarthak, Saberi, Ingmar, Stoica, Bogdan, and Trundy, Brian. 2017.
"Edge length dynamics on graphs with applications to padic AdS/CFT". United States.
doi:10.1007/JHEP06(2017)157. https://www.osti.gov/servlets/purl/1425489.
@article{osti_1425489,
title = {Edge length dynamics on graphs with applications to padic AdS/CFT},
author = {Gubser, Steven S. and Heydeman, Matthew and Jepsen, Christian and Marcolli, Matilde and Parikh, Sarthak and Saberi, Ingmar and Stoica, Bogdan and Trundy, Brian},
abstractNote = {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 EinsteinHilbert 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 padic AdS/CFT, where such a tree takes the place of antide Sitter space. Here, 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.},
doi = {10.1007/JHEP06(2017)157},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2017,
place = {United States},
year = {2017},
month = {6}
}