N=2 Worldsheet Instantons Yield Cubic Self-Dual Yang-Mills

Abstract

When the gauge instantons on the N=2 string worldsheet are properly included in the sum over topologies, the breaking of SO(2,2) Lorentz symmetry in R^{2,2} is parametrized by a spacetime twistor containing the string coupling and theta angle. The resulting (tree-level) effective action for the open string is not Yang's but Leznov's cubic action for self-dual Yang-Mills in a light-cone gauge. In the closed case, Plebanski's action for self-dual gravity gets modified analogously. In contrast to the N=1 NSR string, picture-changing is not locally invertible, but produces a semi-infinite tower of massless physical states with ever-increasing spin, perhaps related to harmonic superspace. A truncation yields the two-field action of Chalmers and Siegel.

9 pages, no figures, LaTeX (amsbsy,latexsym)

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• N=2 Quantum String Scattering
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• Large N WZW Field Theory Of N=2 Strings
• The Effective Action and Geometry of Closed N=2 Strings
• String-induced Yang-Mills coupling to self-dual gravity
• N=2 String Geometry and the Heavenly Equations
• Hidden Symmetries of the Open N=2 String
• $A_{\infty }$ Action of Open $\mathcal{N}=2$ Superstring Field Theory