Matrix Models, Gauge Theory and Emergent Geometry

Understand

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.