Geometry in Transition: A Model of Emergent Geometry

Delgadillo-Blando, Rodrigo, O'Connor, Denjoe and Ydri, Badis (2008) Geometry in Transition: A Model of Emergent Geometry. Physical Review Letters, 100 (20). ISSN 0031-9007

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We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent α = 1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early universe.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:23
Last Modified: 21 Dec 2022 08:43
Identification Number: DIAS-STP-07-22

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