Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
arXiv:2008.07726 · doi:10.1093/ptep/ptab034
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.
arXiv comment23 pages, 9 figures, minor corrections
References in corpus (19)
- 2D Gravity and Random Matrices
- Spin-Glass Theory for Pedestrians
- Emergence of a 4D World from Causal Quantum Gravity
- Critical behavior of colored tensor models in the large N limit
- Quantum Gravity from Causal Dynamical Triangulations: A Review
- Colored Group Field Theory
- The causal set approach to quantum gravity
- Two-Matrix model with ABAB interaction
- Canonical tensor models with local time
- Uniqueness of canonical tensor model with local time
- Interpreting canonical tensor model in minisuperspace
- Quantum canonical tensor model and an exact wave function
- Physical states in the canonical tensor model from the perspective of random tensor networks
- Symmetric configurations highlighted by collective quantum coherence
- Emergent symmetries in the canonical tensor model
- Kazakov--Migdal Model with Logarithmic Potential and the Double Penner Matrix Model
- A random matrix model with non-pairwise contracted indices
- Numerical and analytical analyses of a matrix model with non-pairwise contracted indices
- Phases of a matrix model with non-pairwise index contractions