Supersymmetric string waves

Abstract

We present plane-wave-type solutions of the lowest-order superstring effective action which have unbroken space-time supersymmetries. They are given by a stringy generalization of the Brinkmann metric, dilaton, axion, and gauge fields. Some conspiracy between the metric and the axion field is required. The ${\alpha }^{\prime }$ stringy corrections to the effective on-shell action, to the equations of motion (and therefore to the solutions themselves), and to the supersymmetry transformations are shown to vanish for a special class of these solutions that we call supersymmetric string waves (SSW's). In the SSW solutions, there exists a conspiracy not only between the metric and the axion field, but also between the gauge fields and the metric, since the embedding of the spin connection in the gauge group is required.