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.
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Masuku, M., Mulokwe, M. & Rodrigues, J.P. Large N matrix hyperspheres and the gauge-gravity correspondence. J. High Energ. Phys. 2015, 1–13 (2015). https://doi.org/10.1007/JHEP12(2015)035
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DOI: https://doi.org/10.1007/JHEP12(2015)035