2016/12/30 by Steven S. Gubser, Matthew Heydeman, Christian Jepsen +6 · 58 citations
Computer Science · Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Combinatorics #Constant curvature #Curvature #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Ricci curvature #Topological and Geometric Data Analysis #advanced mathematical theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep06(2017)157
published in Journal of High Energy Physics 2017(6) (Springer Nature) · 42 pages, 6 figures
arxiv created 2016/12/30 · openalex publication_date 2017/06/01 · arxiv updated 2017/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.