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.
Highlights
The application of the functional Renormalization Group (FRG) [1] in the discrete quantum gravity context facilitates a background-independent form of coarse graining where the number of degrees of freedom serves as a scale for an RG flow
There exists a proposed correspondence between a Hermitian two-matrix model with ABAB interaction [6] with causal dynamical triangulations approach (CDT) in 2 + 1 dimensions which leads to a variant of CDT allowing for degeneracies of the local geometry [7]
The essential idea of this model is that causality can be imposed on a matrix model by introducing a second matrix that enables a distinction of space-like and time-like edges in the dual triangulation
Summary
The application of the functional Renormalization Group (FRG) [1] in the discrete quantum gravity context facilitates a background-independent form of coarse graining where the number of degrees of freedom serves as a scale for an RG flow This program was initiated by analyzing matrix and tensor models for Euclidean quantum gravity in d ≥ 2 [2, 3]. The essential idea of this model is that causality can be imposed on a matrix model by introducing a second matrix that enables a distinction of space-like and time-like edges in the dual triangulation. We present this models’ phase structure based on our FRG analysis in [8]
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