De Alfaro, Fubini and Furlan from multi Matrix Systems

TL;DR

This paper explores the quantum mechanics of multi-matrix systems, revealing an emergent radial fermion description with De Alfaro, Fubini, and Furlan potential, and identifying associated symmetries and large N behavior.

Contribution

It introduces a novel radial fermion framework for multi-matrix quantum systems with emergent symmetries and potential structures.

Findings

Emergent De Alfaro, Fubini, and Furlan potential for complex matrix systems.

Identification of $AdS_2$ symmetry in the model.

Large N eigenvalue density description of the system.

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