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Edge length dynamics on graphs with applications to p-adic 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 Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles shoul...

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Main Authors: Gubser, Steven Scott (Author) , Heydeman, Matthew (Author) , Jepsen, Christian (Author) , Marcolli, Matilde (Author) , Parikh, Sarthak (Author) , Saberi, Ingmar (Author) , Stoica, Bogdan (Author) , Trundy, Brian (Author)
Format: Article (Journal)
Language:English
Published: 30 June 2017
In: Journal of high energy physics
Year: 2017, Issue: 6
ISSN:1029-8479
DOI:10.1007/JHEP06(2017)157
Online Access:Verlag, kostenfrei, Volltext: http://dx.doi.org/10.1007/JHEP06(2017)157
Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/JHEP06(2017)157
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Author Notes:Steven S. Gubser, Matthew Heydeman, Christian Jepsen, Matilde Marcolli, Sarthak Parikh, Ingmar Saberi, Bogdan Stoica and Brian Trundy

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520 |a 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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