Colored Tensor Models - a Review

2011

181 citations recorded by the source corpus.

Colored tensor models have recently burst onto the scene as a promising con- ceptual 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 al- gebra 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.

Subfields: Computational Mathematics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fe4ce7c620305e9c95e7e8c926384e573aefc0a2

Citations in the corpus

• Random tensor models in the large N limit: Uncoloring the colored tensor models (2012, unknown): “To every graph B with D colors we can associate a non-negative integer, its degree ω(B) [39, 40, 43].”
• The nonperturbative functional renormalization group and its applications (2020, unknown): “The connection to quantum gravity arises as the Feynman diagrams of such rank-d models are dual to triangulations of d dimensional space, see [1338–1343], see [1344–1350] for reviews.”
• O(N) Random Tensor Models (2015, unknown): “The so-called colored models [1, 2] brought new combinatorial tools to tensor models, which tremendously improved our control over the definition and topological content of such models.”
• The complete 1/N expansion of a SYK–like tensor model (2016, unknown): “With the exception of the first paper on the topic, [9], the CTM is usually formulated for bosonic fields.”
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates (2016, unknown): “gravity degrees of freedom [9], although organized in a different Fock-type Hilbert space, and on the other hand as an enrichment of lattice gravity approaches like tensor models [10] (in turn a higher-dimensional generalization of matrix models for 2D gravity, and closely related to the dynamical t”
• Group field theory as the second quantization of loop quantum gravity (2013, unknown): “Group field theories [1, 2] are a generalization of matrix models and an enrichment of tensor models [3] through the addition of group-theoretic data interpreted as pre-geometric data, ‘seeds’ of the continuum geometry that these models should generate in a continuum approximation.”