<p>We investigate the supersymmetric extension of the generalized Kerr-Schild ansatz (gKSA) in Double Field Theory (DFT) including first-order <i>α</i>′ corrections. Supersymmetry plays a central role in constraining higher-derivative deformations, and in this work we focus on the structure of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{O}(\alpha {\prime})\)</EquationSource> </InlineEquation> Killing Spinor Equations (KSEs). Starting from the <i>α</i>′-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 <i>α</i>′-corrected KSEs. We then provide the explicit parameterization of the results in terms of the ten-dimensional <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{N}=1\)</EquationSource> </InlineEquation> supergravity fields. Our construction establishes a unified framework for exploring supersymmetric backgrounds in <i>α</i>′-corrected DFT and offers new tools for generating higher-derivative supergravity solutions.</p>

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Supersymmetric α′-corrections to the generalized Kerr-Schild ansatz

  • Jesús A. Rodríguez

摘要

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 \(\mathcal{O}(\alpha {\prime})\) 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.