The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization

TL;DR

This paper applies the functional renormalization group method to analyze the phase diagram and fixed points of a multi-matrix model with ABAB-interaction, relevant for 3D Lorentzian quantum gravity, demonstrating the method's effectiveness in discrete quantum gravity models.

Contribution

It characterizes the fixed-point structure and phase diagram of the ABAB-interaction multi-matrix model using functional RG, providing a foundation for studying more complex models.

Findings

Identified fixed points and phase structure of the model.

Validated the functional RG approach in discrete quantum gravity.

Set the stage for analyzing more general tensor models.

Abstract

At criticality, discrete quantum-gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional renormalization group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with $ABAB$-interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality and subjecting the technique to another strong test of its performance in discrete quantum gravity by comparing to known results.