Edge length dynamics on graphs with applications to \(p\)-adic AdS/CFT
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Publication:683289
DOI10.1007/JHEP06(2017)157zbMATH Open1380.83066arXiv1612.09580OpenAlexW2569888289MaRDI QIDQ683289
Author name not available (Why is that?)
Publication date: 5 February 2018
Published in: (Search for Journal in Brave)
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 -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.
Full work available at URL: https://arxiv.org/abs/1612.09580
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