Abstract
The string field theory of N = (2,1) heterotic strings describes a set of self-dual Yang - Mills fields coupled to self-dual gravity in 2 + 2 dimensions. We show that the exact classical action for this field theory is a certain complexification of the Green - Schwarz/Dirac - Born - Infeld string action, closely related to the four-dimensional Wess - Zumino action describing self-dual gauge fields. This action describes the world-volume of a (2 + 2)D `M-brane', which gives rise upon different null reductions to critical strings and membranes. We discuss a number of further properties of N = 2 heterotic strings, such as the geometry of null reduction, general features of a covariant formulation, and possible relations to BPS and GKM algebras.
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