Supersymmetric Soluble Systems Embedded in Supersymmetric Self--Dual Yang--Mills Theory

Abstract

We perform dimensional reductions of recently constructed self-dual $N=2$~ {\it supersymmetric} Yang-Mills theory in $~2+2\-$dimensions into two-dimensions. We show that the universal equations obtained in these dimensional reductions can embed supersymmetric exactly soluble systems, such as $N=1$~ and $N=2$~ supersymmetric Korteweg-de Vries equations, $N=1$~ supersymmetric Liouville theory or supersymmetric Toda theory. This is the first supporting evidence for the conjecture that the $~2+2\-$dimensional self-dual {\it supersymmetric} Yang-Mills theory generates {\it supersymmetric} soluble systems in lower-dimensions.

LATEX 13 pages

References in corpus (1)

• Extended Supersymmetry and Self-Duality in 2+2 Dimensions

Cited by in corpus (16)

• A Study of General 2D, N=2 Matter Coupled to Supergravity in Superspace
• Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations
• Infinite Conformal Algebras in Supersymmetric Theories on Four Manifolds
• Self-Dual Supergravity from N=2 Strings
• Stationary Axisymmetric Black Holes, $N=2$ Superstring, and Self-Dual Gauge or Gravity Fields
• Noncommutative Self-Dual Supersymmetric Yang-Mills Theory
• Supersymmetric KP Systems Embedded in Supersymmetric Self-Dual Yang-Mills Theory
• Exact Solutions for Self--Dual Yang--Mills and Self--Dual Tensor Multiplets on Gravitational Instanton Background
• Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity
• Self-Dual Supersymmetric Yang-Mills Theory Generates Witten's Topological Field Theory
• Self-Dual Supersymmetric Yang-Mills Theory Generates Two-Dimensional Supersymmetric WZNW Models
• Noncommutative Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
• ``Alternative $N=(4,0)$ Superstring and $\s$-Models''
• Self-dual non-Abelian N = 1 tensor multiplet in D = 2+ 2 dimensions
• Self-Dual Yang-Mills and Vector-Spinor Fields, Nilpotent Fermionic Symmetry, and Supersymmetric Integrable Systems
• Two-Dimensional Dilaton Gravity Black Hole Solution for $N=2$ Superstring Theory