Matrix models, gauge theory and emergent geometry

Delgadillo-Blando, Rodrigo, O'Connor, Denjoe and Ydri, Badis (2009) Matrix models, gauge theory and emergent geometry. Journal of High Energy Physics, 2009 (05). 049-049. ISSN 1029-8479

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We present, theoretical predictions and Monte Carlo simulations, for a simple three matrix model that exhibits an exotic phase transition. The nature of the transition is very different if approached from the high or low temperature side. The high temperature phase is described by three self interacting random matrices with no background spacetime geometry. As the system cools there is a phase transition in which a classical two-sphere condenses to form the background geometry. The transition has an entropy jump or latent heat, yet the specific heat diverges as the transition is approached from low temperatures. We find no divergence or evidence of critical fluctuations when the transition is approached from the high temperature phase. At sufficiently low temperatures the system is described by small fluctuations, on a background classical two-sphere, of a U(1) gauge field coupled to a massive scalar field. The critical temperature is pushed upwards as the scalar field mass is increased. Once the geometrical phase is well established the specific heat takes the value 1 with the gauge and scalar fields each contributing 1/2.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:18
Last Modified: 16 Dec 2022 02:23
Identification Number: DIAS-STP-08-24

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