Abstract:The large N dynamics of a subsector of d = 0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, and as a result the density of radial eigenvalues has support on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom of the Yang-Mills interaction can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.
We study the three dimensional O(N) invariant bosonic vector model with a λ N (φ a φ a ) 2 interaction at its infrared fixed point, using a bilocal field approach and in an 1/N expansion. We identify a (negative energy squared) bound state in its spectrum about the large N conformal background. At the critical point this is identified with the ∆ = 2 state. We further demonstrate that at the critical point the ∆ = 1 state disappears from the spectrum. * 1 There is a vast literature on the subject; [5,6,7,8] are representative of the work on the subject, but they do not form by any means an exhaustive list.
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