Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model

TL;DR

This paper investigates a two-logarithm matrix model derived from a tensor model, revealing that symmetry enhancement and stable emergent space dimensions occur only when the cosmological constant is positive, highlighting its significance.

Contribution

It introduces a novel two-logarithm matrix model linked to the canonical tensor model and demonstrates the conditions for symmetry enhancement and stable emergent spaces.

Findings

Symmetry enhancement occurs only in the positive cosmological constant phase.

Stable emergent space dimensions are exclusive to the positive cosmological constant case.

The model suggests the positivity of the cosmological constant is crucial for emergence phenomena.

Abstract

I study a one-matrix model of a real symmetric matrix with a potential which is a sum of two logarithmic functions and a harmonic one. This two-logarithm matrix model is the absolute square norm of a toy wave function which is obtained by replacing the tensor argument of the wave function of the canonical tensor model (CTM) with a matrix. I discuss a symmetry enhancement phenomenon in this matrix model and show that symmetries and dimensions of emergent spaces are stable only in a phase which exists exclusively for the positive cosmological constant case in the sense of CTM. This would imply the importance of the positivity of the cosmological constant in the emergence phenomena in CTM.