Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 068, 36 pages      arXiv:1603.00172
Contribution to the Special Issue on Tensor Models, Formalism and Applications

Exact Renormalisation Group Equations and Loop Equations for Tensor Models

Thomas Krajewski a and Reiko Toriumi b
a) Aix Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 13288 Marseille, France
b) Department of Physics, University of California Berkeley, USA

Received February 29, 2016, in final form July 05, 2016; Published online July 14, 2016

In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading order expectation values of observables in tensor models. Furthermore, we use the exact renormalisation group equations to establish a suitable scaling dimension for interactions in Abelian tensorial group field theories with a closure constraint. We also present analogues of the loop equations for tensor models.

Key words: tensor models; group field theory; large $N$ limit; exact renormalisation equation.

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