Supersymmetric String Waves

TL;DR

This work identifies a broad family of plane-wave-type backgrounds in the ten-dimensional superstring setting that preserve space-time supersymmetry and remain perturbatively exact to all orders in $\alpha'$. By employing a Brinkmann-type metric with flat transverse space and aligning the dilaton, axion, and Yang-Mills fields through a single light-cone vector, the authors derive harmonic constraints in the transverse space and show that a special embedding of the torsionful spin connection into $SO(8)$ cancels all higher-order corrections to both the equations of motion and SUSY transformations. The resulting supersymmetric string waves (SSW) generalize Güven’s exact plane waves and reveal a non-renormalization mechanism tied to the alignment of geometric and gauge data. The findings have potential implications for sigma-model dualities and a new perturbative approach to quantum gravity in highly symmetric, supersymmetric backgrounds.

Abstract

We present plane-wave-type solutions of the lowest order superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a stringy generalization of the Brinkmann metric. Some conspiracy between the metric and the axion field is required. We show that there exists a special class of these solutions, for which $α^\prime$ stringy corrections to the effective on-shell action, to the equations of motion (and therefore to the solutions themselves), and to the supersymmetry transformations vanish. We call these solutions supersymmetric string waves (SSW).