Edge length dynamics on graphs with applications to p-adic AdS/CFT

A bstract 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 cy...

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Bibliographic Details
Published in:The journal of high energy physics 2017-06, Vol.2017 (6), p.1-35, Article 157
Main Authors: Gubser, Steven S., Heydeman, Matthew, Jepsen, Christian, Marcolli, Matilde, Parikh, Sarthak, Saberi, Ingmar, Stoica, Bogdan, Trundy, Brian
Format: Article
Language:English
Subjects:
AdS-CFT Correspondence
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Classical Theories of Gravity
Correlators
Curvature
Elementary Particles
Graphs
High energy physics
Lattice Models of Gravity
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP06(2017)157