Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting

Abstract

In this paper, we use the exact renormalisation in the context of tensor models and tensorial group field theories. As a byproduct, we rederive Gaussian universality for random tensors and provide a general power counting for Abelian tensorial field theories with a closure constraint, leading us to a only five renormalizable theories.

22 pages, 4 figures

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• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Towards background independent quantum gravity with tensor models
• (No) phase transition in tensorial group field theory
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case