Large N Matrix Mechanics on the Light-Cone

TL;DR

This paper simplifies the large N matrix mechanics of light-cone field theories by expressing Hamiltonians in terms of Cuntz algebra generators, revealing new conserved quantities and simplifying eigenvalue problems.

Contribution

It introduces a novel free-algebraic framework for large N matrix models using Cuntz algebra, uncovering hidden conserved quantities and simplifying spectral analysis.

Findings

Explicit large N Hamiltonians as functions of Cuntz algebra generators

Discovery of new hidden conserved quantities at large N

Simplification of eigenvalue problems for these models

Abstract

We report a simplification in the large N matrix mechanics of light-cone matrix field theories. The absence of pure creation or pure annihilation terms in the Hamiltonian formulation of these theories allows us to find their reduced large N Hamiltonians as explicit functions of the generators of the Cuntz algebra. This opens up a free-algebraic playground of new reduced models -- all of which exhibit new hidden conserved quantities at large N and all of whose eigenvalue problems are surprisingly simple. The basic tool we develop for the study of these models is the infinite dimensional algebra of all normal-ordered products of Cuntz operators, and this algebra also leads us to a special number-conserving subset of these models, each of which exhibits an infinite number of new hidden conserved quantities at large N.