The N=2 supersymmetric Toda lattice and matrix models

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.

22 pages, Latex

References in corpus (5)

• Toward the construction of N=2 supersymmetric integrable hierarchies
• The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy
• The Discrete Symmetry of the N=2 Supersymmetric Modified NLS Hierarchy
• The Solution of the N=2 Supersymmetric f-Toda Chain with Fixed Ends
• N=2 Superintegrable f-Toda Mapping and Super-NLS Hierarchy in the (1|2) Superspace

Cited by in corpus (2)

• Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
• Generalized fermionic discrete Toda hierarchy