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SIGMA, 2012, Volume 8, 020, 78 pages (Mi sigma697)  

This article is cited in 165 scientific papers (total in 165 papers)

Colored tensor models – a review

Razvan Guraua, James P. Ryanb

a Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo, Canada
b MPI für Gravitationsphysik, Albert Einstein Institute, Am Mühlenberg 1, D-14476 Potsdam, Germany

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 two-dimensional 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.

Keywords: colored tensor models, $1/N$ expansion.


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ArXiv: 1109.4812
MSC: 05C15; 05C75; 81Q30; 81T17; 81T18; 83C27; 83C45
Received: October 5, 2011; in final form March 13, 2012; Published online April 10, 2012

Citation: Razvan Gurau, James P. Ryan, “Colored tensor models – a review”, SIGMA, 8 (2012), 020, 78 pp.

Citation in format AMSBIB
\by Razvan Gurau, James P. Ryan
\paper Colored tensor models -- a review
\jour SIGMA
\yr 2012
\vol 8
\papernumber 020
\totalpages 78

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