The target space geometry of N=(2,1) string theory

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We describe the O(α'⁰) constraints on the target space geometry of the N=(2,1) heterotic superstring due to the left-moving N=1 supersymmetry and U(1) currents. In the fermionic description of the internal sector supersymmetry is realized quantum mechanically, so that both tree-level and one-loop effects contribute to the order O(α'⁰) constraints. We also discuss the physical interpretation of the resulting target space geometry in terms of configurations of a 2+2-dimensional object propagating in a 10+2-dimensional spacetime with a null isometry, which has recently been suggested as a unified description of string and M theory.