Large $N$ Phase Transition In The Heat Kernel On The $U(N)$ Group

Details Large $N$ Phase Transition In The Heat Kernel On The $U(N)$ Group Large $N$ Phase Transition In The Heat Kernel On The $U(N)$ Group

1994-10-12

arxiv.org/abs/hep-th/9410087v1

Nucl.Phys. B440 (1995) 407-420

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LPTENS-94/28

Scientific paper

10.1016/0550-3213(95)00077-6

The large N phase transition point is investigated in the heat kernel on the $U(N)$ group with respect to arbitrary boundary conditions. A simple functional relation is found relating the density of eigenvalues of the boundary field to the saddle point shape of the typical Young tableaux in the large $N$ limit of the character expansion of the heat kernel. Both strong coupling and weak coupling phases are investigated for some particular cases of the boundary holonomy.

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