Colored Tensor Models  a Review
Abstract
Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating twodimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, SchwingerDyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions), nontrivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
 Publication:

SIGMA
 Pub Date:
 April 2012
 DOI:
 10.3842/SIGMA.2012.020
 arXiv:
 arXiv:1109.4812
 Bibcode:
 2012SIGMA...8..020G
 Keywords:

 colored tensor models;
 1/N expansion;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 05C15;
 05C75;
 81Q30;
 81T17;
 81T18;
 83C27;
 83C45
 EPrint:
 SIGMA 8 (2012), 020, 78 pages