Colored Tensor Models - a Review

• Published in: Symmetry, integrability and geometry, methods and applications Vol. 8; p. 020
• Main Author: Gurau, Razvan
• Format: Journal Article
• Language: English
• Published: Kiev National Academy of Sciences of Ukraine 01.01.2012; National Academy of Science of Ukraine
• Subjects: 1/N expansion; colored tensor models
• ISSN: 1815-0659; 1815-0659
• DOI: 10.3842/SIGMA.2012.020

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. [ProQuest: [...] denotes formulae omitted.]