  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.
