Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly

Understand

The equations that follow from kappa symmetry of the type II Green-Schwarz string are a certain deformation, by a Killing vector field $K$, of the type II supergravity equations.

• We analyze under what conditions solutions of these `generalized' supergravity equations are trivial in the sense that they solve also the standard supergravity equations.
• We argue that for this to happen $K$ must be null and satisfy $dK=i_KH$ with $H=dB$ the NSNS three-form field strength.
• Non-trivial examples are provided by symmetric pp-wave solutions.