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arXiv · 1509.03572

Emergent geometry from random multitrace matrix models

B. Ydri·A. Rouag·K. Ramda
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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.

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B. Ydri, A. Rouag, K. Ramda. 2015-09-11. Emergent geometry from random multitrace matrix models. https://doi.org/10.1103/physrevd.93.065055

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