Symmetries, Currents and Conservation Laws of Self-Dual Gravity

Abstract

We describe an infinite-dimensional algebra of hidden symmetries for the self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w(infinity) algebra), this algebra contains new hidden symmetries, which are an affine extension of the Lorentz rotations. The full symmetry algebra has both Kac-Moody and Virasoro-like generators, whose exponentiation maps solutions of the field equations to other solutions. Relations to problems of string theories are briefly discussed.

14 pages, LaTeX, the paper was reformatted

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• The Kinematic Algebra From the Self-Dual Sector
• Chiral Higher Spin Theories and Self-Duality
• Double Copy from Homotopy Algebras
• A double copy for asymptotic symmetries in the self-dual sector
• Self-Dual Yang-Mills: Symmetries and Moduli Space
• On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Hydrodynamic reductions of the heavenly equation
• Self-Dual Supergravity and Twistor Theory
• M-branes and N=2 Strings
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Holomorphic Chern-Simons-Witten Theory: from 2D to 4D Conformal Field Theories
• Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries
• On Infinite-Dimensional Algebras of Symmetries of the Self-Dual Yang-Mills Equations
• Non-local symmetries of the closed N=2 string
• Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy
• An action of N=8 self-dual supergravity in ultra-hyperbolic harmonic superspace
• Large N WZW Field Theory Of N=2 Strings
• Ward identities and the vanishing theorem for loop amplitudes of the closed N=2 string
• Large N Field Theory of N=2 Strings and Self-Dual Gravity