De Alfaro, Fubini and Furlan from multi Matrix Systems

Understand

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 $AdS_2$ symmetry is identified.
• The large $N$ description in terms of the density of radial eigenvalues is also described.