Emergent geometry from random multitrace matrix models

Abstract

A novel scenario for the emergence of geometry in random multitrace matrix models of a single hermitian matrix $M$ with unitary $U(N)$ invariance, i.e. without a kinetic term, is presented. In particular, the dimension of the emergent geometry is determined from the critical exponents of the disorder-to-uniform-ordered transition whereas the metric is determined from the Wigner semicircle law behavior of the eigenvalues distribution of the matrix $M$. If the uniform ordered phase is not sustained in the phase diagram then there is no emergent geometry in the multitrace matrix model.

18 pages, 7 figures (16 graphs), 1 table

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Cited by in corpus (7)

• Matrix Model Approach to Cosmology
• Lectures on Matrix Field Theory I
• A Multitrace Approach to Noncommutative Φ_2^4
• Quantum Gravity as a Multitrace Matrix Model
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• The multitrace matrix model: An alternative to Connes NCG and IKKT model
• Wilsonian Matrix Renormalization Group