Real fermionic symmetry in type II supergravity

It is known that the transformations of fermionic T-duality, derived from the worldsheet theory, generically transform real supergravity backgrounds to complex supergravity backgrounds. We consider the low-energy target space theory and show that the type II supergravity equations admit a symmetry that transforms the Ramond-Ramond fields and the dilaton. The transformations given by this symmetry involve Killing spinors and include the transformations of Berkovits and Maldacena. However, we show that they also allow real transformations.