Phase structure of matrix quantum mechanics at finite temperature

Details Phase structure of matrix quantum mechanics at finite temperature Phase structure of matrix quantum mechanics at finite temperature

2007-06-25

arxiv.org/abs/0706.3517v2

JHEP0710:097,2007

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 9 figures, (v2) refined arguments in section 3 ; reference added

Scientific paper

10.1088/1126-6708/2007/10/097

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N=32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.

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