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


SIGMA 8 (2012), 020, 78 pages      arXiv:1109.4812      http://dx.doi.org/10.3842/SIGMA.2012.020
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Colored Tensor Models - a Review

Razvan Gurau a and James P. Ryan b
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

Received October 05, 2011, in final form March 13, 2012; Published online April 10, 2012

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.

Key words: colored tensor models; 1/N expansion.

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