Lost in translation: topological singularities in group field theory

By R. Gurau. 2010

155 citations recorded by the source corpus.

Random matrix models generalize to group field theories (GFTs) whose Feynman graphs are dual to gluings of higher dimensional simplices. It is generally assumed that GFT graphs are always dual to pseudo manifolds. In this paper, we prove that already in dimension three (and in all higher dimensions), this is not true due to subtle differences between simplicial complexes and gluings dual to GFT graphs. We prove however that, fortunately, the recently introduced ‘colored’ GFT models (Gurau R 2009 arXiv:0907.2582 [hep-th]) do not suffer from this problem and only generate graphs dual to pseudo manifolds in any dimension.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a9906fe24bc2437cc9a84d522e5a2d22b6705296

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Citations in the corpus

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”
Zakopane lectures on loop gravity (2011, background): “But there are also ideas and interesting attempts to interpret knotting and linking as matter degrees of freedom [37, 38, 39].”
The 1/N Expansion of Colored Tensor Models (2010, background): “If all its bubbles are planar, then it is dual to an orientable manifold [ 25 ].”
A Renormalizable 4-Dimensional Tensor Field Theory (2011, unknown): “We refer to [44] for a review and to [45, 46, 47, 48] for other results or aspects of this thriving subject.”
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.”