Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

By Sylvain Carrozza, D. Oriti, Vincent Rivasseau. 2012

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We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a445ca4f73ac43dc8d979c0de8399252674596a8

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Citations in the corpus

O(N) Random Tensor Models (2015, background): “[25] Sylvain Carrozza, Daniele Oriti, and Vincent Rivasseau.”
The continuum limit of loop quantum gravity - a framework for solving the theory (2014, background): “triangulations and hopes to achieve a continuum limit by choosing weights such that conﬁgurations with inﬁnitely many building blocks dominate [72]. The relation between renormalization in a gft sense[73], which involves an explicit scale, and the coarse graining scheme presented here should be bett”