Supersymmetric $α'$-corrections to the Generalized Kerr-Schild Ansatz

TL;DR

This work develops a supersymmetric extension of the generalized Kerr-Schild Ansatz within Double Field Theory, including first-order $\alpha'$ corrections. It derives the $\mathcal{O}(\alpha')$ Killing spinor equations and shows how generalized Green–Schwarz transformations constrain perturbations to achieve linearization. The authors parameterize the results in terms of $D=10$, ${\cal N}=1$ supergravity fields, providing a bridge between DFT and conventional supergravity. The framework facilitates constructing $\alpha'$-corrected supersymmetric backgrounds and may illuminate higher-derivative string background solutions.

Abstract

We investigate the supersymmetric extension of the generalized Kerr-Schild ansatz (gKSA) in Double Field Theory (DFT) including first-order $α'$ corrections. Supersymmetry plays a central role in constraining higher-derivative deformations, and in this work we focus on the structure of the $\mathcal{O}(α')$ Killing Spinor Equations (KSEs). Starting from the $α'$-corrected supersymmetry transformations of the fermionic fields, we derive the corresponding KSEs in DFT and analyze their behavior under the gKSA. The generalized Green-Schwarz transformations impose specific constraints on the perturbations that ensure the linearization of the $α'$-corrected KSEs. We then provide the explicit parameterization of the results in terms of the ten-dimensional $\mathcal{N}=1$ supergravity fields. Our construction establishes a unified framework for exploring supersymmetric backgrounds in $α'$-corrected DFT and offers new tools for generating higher-derivative supergravity solutions.