Causal dynamical triangulation of a 3D tensor model

Abstract

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.

17pages,12figures, typos corrected

References in corpus (8)

• Random tensor models in the large N limit: Uncoloring the colored tensor models
• A String Field Theory based on Causal Dynamical Triangulations
• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• A new continuum limit of matrix models
• Stochastic quantization and the role of time in quantum gravity
• Causal Dynamical Triangulation with Extended Interactions in 1+1 Dimensions
• Stochastic Quantization Approach for Causal Dynamical Triangulation String Field Theory
• Causal dynamical triangulation for non-critical open-closed string field theory

Cited by in corpus (1)

• CDT open-closed surface field theory of a 3D tensor-matrix model