Colored Group Field Theory

By R. Gurau. 2009

355 citations recorded by the source corpus.

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to higher dimensional topological spaces. The perturbative development of the usual GFT’s is rather involved combinatorially and plagued by topological singularities (which we discuss in great detail in this paper), thus very difficult to control and unsatisfactory.Both these problems simplify greatly for the “colored” GFT (CGFT) model we introduce in this paper. Not only this model is combinatorially simpler but also it is free from the worst topological singularities. We establish that the Feynman graphs of our model are combinatorial cellular complexes dual to manifolds or pseudomanifolds, and study their cellular homology. We also relate the amplitude of CGFT graphs to their fundamental group.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/08b07b6772786a03a249f64001d525995fb98b25

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Citations in the corpus

Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models (2017, neutral): “For example, in SYK model it denotes the ‘flavour indices’ of fermions ψi, while in Witten-Gurau model it denotes the tri-fundamental index the fermions carry.”
The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension (2011, methodology): “(25) The amplitude of G ,i s [1,43, 46 ] A BO (G )= (λ¯)”
An introduction to the SYK model (2018, methodology): “of the Gurau-Witten model [19, 20] (see also [21–24]), with the Lagrangian,”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “In a further modification of the previous model (known as colored tensor models [208]) new techniques based on a suitable 1/N expansion imply that amplitudes are dominated by spherical topology [207]; moreover, it seem possible that the continuum limit might be critical, as in certain matrix models ”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, background): “The first one is the introduction of colors [67] labelling a multiplet of TGFT fields.”
Random tensor models in the large N limit: Uncoloring the colored tensor models (2012, background): “The (3+1)-colored graphs are known to describe topological 3-dimensional pseudo-manifolds [34].”
All point correlation functions in SYK (2017, background): “These have arisen in a number of independent contexts, including: models of Bose fluids [2], models of spin glasses [3], and tensor models [4].”
Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models (2016, background): “Gurau’s original example [8] was a so-called colored tensor model where complex fermionic tensors ψ1m A carry an additional label A which takes m + 1 possible values 0, 1, .”
The complete 1/N expansion of a SYK–like tensor model (2016, methodology): “With the exception of the first paper on the topic, [9], the CTM is usually formulated for bosonic fields.”
A Renormalizable 4-Dimensional Tensor Field Theory (2011, methodology): “The interaction part of the action is the standard colored action in 4 dimensions [37]”
O(N) Random Tensor Models (2015, background): “…Talence, France 2H. Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125 Magurele, Romania 3IUF, 1 rue Descartes, 75231 Paris Cedex 05 We define in this paper a class of three indices tensor models, endowed with O(N)⊗3 invariance (N being the size of the tensor).”
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.”
The 1/N Expansion of Colored Tensor Models (2010, methodology): “The partition function of the colored Boulatov model [ 23 ]o verG is the path integral”