Year: 2012
Type: article
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, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions), non-trivial 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.
Author: Razvan Gurau
Institution: Perimeter Institute
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2116642797