Self-Dual Supersymmetry and Supergravity in Atiyah-Ward Space-Time

Abstract

We study supersymmetry and self-duality in a four-dimensional space-time with the signature (2,2), that we call the Atiyah-Ward space-time. Dirac matrices and spinors, in particular Majorana-Weyl spinors, are investigated in detail. We formulate $N\ge 1$ supersymmetric self-dual Yang-Mills theories and self-dual supergravities. An N=1 ``self-dual'' tensor multiplet is constructed and a possible ten-dimensional theory that gives rise to the four-dimensional self-dual supersymmetric theories is found. Instanton solutions are given as the zero modes in the N=2 self-dual Yang-Mills theory. The N=2 superstrings are conjectured to have no possible counter-terms at quantum level to all orders. These self-dual supersymmetric theories are to generate exactly soluble supersymmetric systems in lower dimensions.

61 pages

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• Some new integrable equations from the self-dual Yang-Mills equations
• BPS-type equations in the non-anticommutative N=2 supersymmetric U(1) gauge theory
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• The Geometry of $N=2$ Strings with Torsion
• 4D, N=1 Born-Infeld supergravity
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• Einstein Supergravity and New Twistor String Theories
• Sigma Models with N=8 Supersymmetries in 2+1 and 1+1 Dimensions
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• Stationary Axisymmetric Black Holes, $N=2$ Superstring, and Self-Dual Gauge or Gravity Fields
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• N=1/2 supersymmetric four-dimensional non-linear sigma-models from non-anti-commutative superspace
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• W Gravity, $N=2$ Strings and $2+2S{U}^{\ast }(\infty )$
• Noncommutative Self-Dual Supersymmetric Yang-Mills Theory
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• Supersymmetric KP Systems Embedded in Supersymmetric Self-Dual Yang-Mills Theory
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• Self-Dual N=(1,0) Supergravity in Eight Dimensions with Reduced Holonomy Spin(7)
• Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity
• N=1 Super-${\tau }_3$QED from Atiyah-Ward Space-Time
• Exact Solutions for Self--Dual Yang--Mills and Self--Dual Tensor Multiplets on Gravitational Instanton Background
• Towards a stringy extension of self-dual super Yang-Mills
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• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• C-deformation of Supergravity
• ``Alternative $N=(4,0)$ Superstring and $\s$-Models''
• Self-Dual Yang-Mills and Vector-Spinor Fields, Nilpotent Fermionic Symmetry, and Supersymmetric Integrable Systems
• From N=2 strings to F&M theory
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• The *Report
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• Gauge supergravity in $D=2+2$