Exact Renormalisation Group Equations and Loop Equations for Tensor Models

Thomas Krajewski (1, 2) , Reiko Toriumi (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E4 Gravité quantique

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.

Mots clés: tensor models; group field theory; large N limit; exact renormalisation equation

Domaines: Physique mathématique [math-ph]

Thomas Krajewski, Reiko Toriumi. Exact Renormalisation Group Equations and Loop Equations for Tensor Models. Symmetry, Integrability and Geometry : Methods and Applications, 2016, 12, pp.68. ⟨10.3842/SIGMA.2016.068⟩. ⟨hal-01363472⟩