Emergent quantum geometry from stochastic random matrices
| Autor: | Fukuma, Masafumi, Matsumoto, Nobuyuki |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Towards formulating quantum gravity, we present a novel mechanism for the emergence of spacetime geometry from randomness. In [arXiv:1705.06097], we defined for a given Markov stochastic process "the distance between configurations," which enumerates the difficulty of transition between configurations. In this article, we consider stochastic processes of large-$N$ matrix models, where we regard the eigenvalues as spacetime coordinates. We investigate the distance for the effective stochastic process of one-eigenvalue, and argue that this distance can be interpreted in noncritical string theory as probing a classical geometry with a D-instanton. We further give an evidence that, when we apply our formalism to a tempered stochastic process of $U(N)$ matrix, where the 't Hooft coupling is treated as another dynamical variable, a Euclidean AdS$_2$ geometry emerges in the extended configuration space in the large-$N$ limit, and the horizon corresponds to the Gross-Witten-Wadia phase transition point. Comment: 10 pages, 3 figures, talk presented at Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25 September 2019, Corfu, Greece |
| Databáze: | arXiv |
| Externí odkaz: |
|