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

TL;DR

This paper demonstrates that including N=2 worldsheet instantons in string theory modifies the effective action to a cubic form for self-dual Yang-Mills, revealing new insights into spacetime symmetries and physical states.

Contribution

It shows how N=2 string instantons lead to a cubic self-dual Yang-Mills action and introduces a novel tower of massless states with increasing spin.

Findings

Effective action becomes Leznov's cubic form for self-dual Yang-Mills.

Spacetime symmetry breaking is parametrized by a twistor involving string coupling and theta angle.

A tower of massless states with increasing spin emerges from picture-changing.

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.