M-branes and N=2 Strings

TL;DR

This paper explores the classical action of N=(2,1) heterotic string field theory, revealing its relation to M-branes, self-dual fields, and reductions to strings and membranes in 2+2 dimensions.

Contribution

It introduces a complexified Green-Schwarz/Dirac-Born-Infeld action describing an M-brane in 2+2 dimensions and discusses its properties and reductions.

Findings

Exact classical action identified as a complexification of known string actions

M-brane world-volume described by this action in 2+2 dimensions

Connections to null reductions, BPS, and GKM algebras discussed

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+2d ``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.