Laboratoire de Physique Théorique de l'É'cole Normale Superiéure, 24 rue Lhomond, 75231, Paris Cedex 05, France
Abstract:
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.