Closed equations of the two-point functions for tensorial group field theory

Abstract

In this paper, we provide the closed equations that satisfy two-point correlation functions of rank 3 and 4 tensorial group field theory. The formulation of the current problem extends the method used by Grosse and Wulkenhaar (2009 arXiv:0909.1389) to the tensor case. Ward–Takahashi identities and Schwinger–Dyson equations are combined to establish a nonlinear integral equation for the two-point functions. In the three-dimensional case, the solution of this equation is given perturbatively at the second order of the coupling constant.