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Finite temperature phase transitions in the quenched BFSS matrix model Yewchuk, Simon Andrew

Abstract

A lattice Monte Carlo simulation of the BFSS matrix model of M-theory with fermions removed is discussed. It is expected that a Hagedorn/deconfmement type phase transition exists in this model and that the deconfined state is related to the black hole states of type IIA supergravity. The black hole phase is expected to be recovered in the 't Hooft large N limit of the BFSS model. The numerical simulation is constructed by investigating the behaviour of various toy models, using the Polyakov loop as an order parameter for the transition. A Fadeev-Popov gauge fixing is used to handle the gauge fields. A first order phase transition behaviour can readily be seen in this model. At finite N it appears as an analytic step function which is expected to become a true step function in the large .N limit. The final Monte Carlo simulations are done on a twenty site lattice, using a value of N = 40. The phase diagram of the transition is mapped out for dimensions two through nine and the phase behaviour for nine dimensions is investigated for when a mass term is added to the action. The phase behaviour of a related model - the pp-wave matrix model - is also discussed.

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