The N=2 supersymmetric Toda lattice and matrix models

TL;DR

This paper introduces a new integrable N=2 supersymmetric Toda lattice hierarchy, providing its mathematical structures and exploring its potential for supersymmetric matrix models and generalized hierarchies.

Contribution

It defines the hierarchy's Hamiltonian structures, recursion operator, and Lax pairs, and explores its algebraic properties and bosonic limit, advancing supersymmetric integrable systems.

Findings

Defined the hierarchy's Hamiltonian structures and Lax pairs

Provided evidence for an infinite-dimensional N=2 superalgebra of flows

Introduced new Lax representations for the bosonic Toda lattice

Abstract

We propose a new integrable N=2 supersymmetric Toda lattice hierarchy which may be relevant for constructing a supersymmetric one-matrix model. We define its first two Hamiltonian structures, the recursion operator and Lax--pair representation. We provide partial evidence for the existence of an infinite-dimensional N=2 superalgebra of its flows. We study its bosonic limit and introduce new Lax-pair representations for the bosonic Toda lattice hierarchy. Finally we discuss the relevance this approach for constructing N=2 supersymmetric generalized Toda lattice hierarchies.