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Is Group Field Theory fat?

  1. Oct 4, 2009 #1

    atyy

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    http://arxiv.org/abs/0905.3772
    Group field theory renormalization - the 3d case: power counting of divergences
    Laurent Freidel, Razvan Gurau, Daniele Oriti
    "A 3D GFT graph G is a fat graph"

    http://arxiv.org/abs/hep-th/9306153
    2D Gravity and Random Matrices
    P. Di Francesco, P. Ginsparg, J. Zinn-Justin
    "Such diagrams do not yet have enough structure to specify a Riemann surface. The additional structure is given by widening the propagators to ribbons (to give so-called ribbon graphs or “fatgraphs”)."

    http://arxiv.org/abs/0809.2393
    Explicit tensor network representation for the ground states of string-net models
    O. Buerschaper, M. Aguado, G. Vidal
    "A crucial device in the formulation of these models is the fat lattice, which allows an interpretation of the lattice model in terms of a theory in the continuum"
     
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  3. Oct 4, 2009 #2

    atyy

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    Just a bit more background. I came across the possible link between Group Field Theory and Wen's models in Oriti's http://arxiv.org/abs/0710.3276:

    "geometrogenesis ... This is the catchy name given in [43] to a conjectured phase transition of a combinatorial and algebraic model of quantum space described by a a labelled graph, much alike spin networks, between a high-temperature ‘pre-geometric phase’in which space has the form of a complete graph, and thus no notion of locality or geometry (e.g. distance), to a ‘geometric phase’in which the graph acquires a more regular, local structure, where geometric data can be identified. Furthermore, the data labelling the graph then allow for the emergence of matter degrees of freedom, having the role of qausi-particle moving on the resulting regular lattice, in the same way as the model of topological order studied by Wen et al [44] does, in terms of string condensation."

    "This probably means we have been un-cautious enough already." :rofl:

    "The hope is also that the reader will then join the efforts of researchers working in this area, and contribute to turning the present speculations into solid results, in the conviction that most of the many impressive results already obtained in this fascinating field have been just tentative suggestions or speculations at an earlier stage."
     
  4. Oct 4, 2009 #3

    atyy

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    Reading marcus's latest update https://www.physicsforums.com/showthread.php?t=7245&page=62 I can make even more bizarre associations with the Buerschaper et al paper mentioned in the OP.

    Tanasa, http://arxiv.org/abs/0909.5631 "Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with quantum field theory, from a combinatorial point of view."

    Buerschaper et al http://arxiv.org/abs/0809.2393 "The first such proposal was Kitaev's paper [1], where the Abelian toric code was introduced, and a class of non-Abelian generalisations, the quantum double models, with roots in the theory of Hopf algebras. These are examples of gauge models with discrete gauge group [4, 5].
     
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