Causal dynamical triangulation of a 3D tensor model

TL;DR

This paper extends 2D generalized causal dynamical triangulation string field theory to a 3D surface field model using tensor models and stochastic quantization, highlighting unique quantum effects with IK-type interactions.

Contribution

It introduces a 3D tensor model for surface fields based on the loop gas model and applies stochastic quantization, revealing new quantum effects with exclusive IK-type interactions.

Findings

In the double-scaling limit, the model is characterized by two scaling dimensions.

The continuum GCDT model with IK-type interaction is realized with specific restrictions.

The 3D model's quantum effects contain only IK-type interactions, excluding splitting interactions.

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.