$\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz

Abstract

We construct the $\mathcal{N}=1$ supersymmetric extension of the generalized Kerr-Schild ansatz in the flux formulation of Double Field Theory. We show that this ansatz is compatible with $\mathcal{N}=1$ supersymmetry as long as it is not written in terms of generalized null vectors. Supersymmetric consistency is obtained through a set of conditions that imply linearity of the generalized gravitino perturbation and unrestricted perturbations of the generalized background dilaton and dilatino. As a final step we parametrize the previous theory in terms of the field content of the low energy effective $10$-dimensional heterotic supergravity and we find that the perturbation of the $10$-dimensional vielbein, Kalb-Ramond field and gravitino can be written in terms of a pair of null vectors, as expected.

arXiv comment34 pages. We include the gauge sector and applications considering gaugino condensation

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• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Black Hole Horizons from the Double Copy
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• ${\alpha }^{\prime }$-corrections and their double formulation
• Note on the asymptotic structure of Kerr-Schild form
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
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• Kerr-Schild Double Copy of the Randall-Sundrum Black String