N = 1 supersymmetric Double Field Theory and the generalized Kerr-Schild ansatz

Abstract

We construct the 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 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, gauge field, gravitino and gaugino can be written in terms of vectors, as expected.