De Alfaro, Fubini and Furlan from multi Matrix Systems

Abstract

We consider the quantum mechanics of an even number of space indexed hermitian matrices. Upon complexification, we show that a closed subsector naturally parametrized by a matrix valued radial coordinate has a description in terms of non interacting $s$-state "radial fermions" with an emergent De Alfaro, Fubini and Furlan type potential, present only for two or more complex matrices. The concomitant $Ad{S}_2$ symmetry is identified. The large $N$ description in terms of the density of radial eigenvalues is also described.

Citation added; 19 pages

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