TY - JOUR
T1 - Edge length dynamics on graphs with applications to p-adic AdS/CFT
AU - Gubser, Steven S.
AU - Heydeman, Matthew
AU - Jepsen, Christian
AU - Marcolli, Matilde
AU - Parikh, Sarthak
AU - Saberi, Ingmar
AU - Stoica, Bogdan
AU - Trundy, Brian
PY - 2017/6/1
Y1 - 2017/6/1
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Classical Theories of Gravity
KW - Lattice Models of Gravity
UR - http://www.scopus.com/inward/record.url?scp=85021657776&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85021657776&partnerID=8YFLogxK
U2 - 10.1007/JHEP06(2017)157
DO - 10.1007/JHEP06(2017)157
M3 - Article
AN - SCOPUS:85021657776
VL - 2017
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 6
M1 - 157
ER -