Causal dynamical triangulation of a 3D tensor model

We extend the string field theory of 2D generalized causal dynamical triangulation (GCDT) with the Ishibashi-Kawai-type (IK-type) interaction formulated by the matrix model to the 3D model of the surface field theory. Based on the loop gas model, we construct a tensor model for the discretized surface field and then apply it the stochastic quantization method. In the double-scaling limit, the model is characterized by two scaling dimensions D and D-N, the power indices of the minimal length as the scaling parameter. The continuum GCDT model with the IK-type interaction is realized with a similar restriction in the D-N - D space to the 2D model. The distinct property in the 3D model is that the quantum effect contains the IK-type interaction only, while the ordinary splitting interaction is excluded.