Self-Duality in 3+3 Dimensions and the KP Equation

Abstract

We consider two types of generalized self-duality conditions for Yang-Mills fields on paracomplex manifolds of arbitrary dimension. We then specialize to $3+3$ dimensions and show how one can obtain the KP equation from these self-duality conditions on $SL(2,R)$ valued gauge fields.

Plain Tex, 12 pages, UR-1259, ER-40685-711, CTP TAMU-31/92

Cited by in corpus (8)

• Super Yang-Mills in (11,3) Dimensions
• Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8
• W Gravity, $N=2$ Strings and $2+2S{U}^{\ast }(\infty )$
• Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2
• Self-Dual N=(1,0) Supergravity in Eight Dimensions with Reduced Holonomy Spin(7)
• 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
• The emergent nature of time and the complex numbers in quantum cosmology