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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,
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.
