Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 076, 27 pages      arXiv:1603.07220      https://doi.org/10.3842/SIGMA.2016.076
Contribution to the Special Issue on Tensor Models, Formalism and Applications

$(D+1)$-Colored Graphs - a Review of Sundry Properties

James P. Ryan
Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands

Received March 18, 2016, in final form July 25, 2016; Published online August 02, 2016

Abstract
We review the combinatorial, topological, algebraic and metric properties supported by $(D+1)$-colored graphs, with a focus on those that are pertinent to the study of tensor model theories. We show how to extract a limiting continuum metric space from this set of graphs and detail properties of this limit through the calculation of exponents at criticality.

Key words: colored graph theory; random tensors; quantum gravity.

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