A new class of Matrix Models arising from the W-infinity Algebra

TL;DR

This paper introduces a novel class of hermitian matrix models derived from the W-infinity algebra, with applications in bosonization of one-dimensional quantum systems and a plasma interpretation of their thermodynamic limit.

Contribution

It establishes a new connection between W-infinity algebra polynomials and orthogonal bases of matrix models, enabling full bosonization of 1D systems including all perturbative orders.

Findings

Polynomials from W-infinity generators form an orthogonal basis for new matrix models.

Potentials of these models are explicitly derived and interpreted thermodynamically.

Application to all-order bosonization of free fermionic fields on a lattice.

Abstract

We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a class of random hermitian matrix models. The corresponding potentials are given, and the thermodynamic limit interpreted in terms of a simple plasma picture. The new matrix models can be successfully applied to the full bosonization of interesting one-dimensional systems, including all the perturbative orders in the inverse size of the system. As a simple application, we present the all-order bosonization of the free fermionic field on the one-dimensional lattice.