The 1/N Expansion of Colored Tensor Models

By R. Gurau. 2010

297 citations recorded by the source corpus.

In this paper, we perform the 1/N expansion of the colored three-dimensional Boulatov tensor model. As in matrix models, we obtain a systematic topological expansion, with increasingly complicated topologies suppressed by higher and higher powers of N. We compute the first orders of the expansion and prove that only graphs corresponding to three spheres S3 contribute to the leading order in the large N limit.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/50298d3d0ffdf5336993fd7ca5efc4c306ec0fc9

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In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Universality for Random Tensors (2011, background): “The situation has drastically changed recently and the necessary ingredients for universality have been found for tensors of higher rank, with the discovery of the 1/N expansion [19,20,23] for colored [18,21] random tensors.”
Random tensor models in the large N limit: Uncoloring the colored tensor models (2012, background): “Leading order graphs triangulate the D-dimensional sphere in any dimension [38, 39].”
O(N) Random Tensor Models (2015, methodology): “Unlike in [3, 40] the jacket of a connected graph is not necessarily connected – see Fig.”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, background): “The second key result is the TGFT analogue of the 1/N expansion of matrix models identified in [73–75].”
The nonperturbative functional renormalization group and its applications (2020, background): “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.”
An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, background): “A universal continuum limit might exist if the couplings are tuned to critical values while the tensor size N is taken to infinity (Gurau, 2011).”
A Renormalizable 4-Dimensional Tensor Field Theory (2011, methodology): “We now introduce a new tool to study of the divergence degree, namely a sequence of contractions which generalizes the idea of dipole contraction [38, 59, 60].”
The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension (2011, methodology): “The partition function of the D dimensional colored GFT [ 1 ,46,48 ]i s defined by the path integral”