SUSY and tri-vector deformations

We analyze conditions for a tri-vector deformation of a supergravity background to preserve some supersymmetry. Working in the formalism of the SL(5) exceptional field theory, we present its supersymmetry transformations and introduce an additional USp(4) transformation to stay in the supergravity frame. This transformation acts on local indices and deforms BPS equations of exceptional field theory. The requirement for the deformation to vanish is the desired condition. The condition is shown to be consistent with previous results on bi-vector deformations.