Geometries with twisted spheres and non-abelian T-dualities

Spectral flow in two-dimensional field theories is known to correspond to geometrical twisting between two circles in the gravity dual. We generalize this operation to the geometries which have SO(k+1) x SO(k+1) isometries with k>1 and perform various non-abelian T-dualities of the resulting twisted backgrounds. Combination of non-abelian twists and dualities leads to a new solution generating technique in supergravity, and we apply it to the geometries dual to supersymmetric states in N=4 super-Yang-Mills theory.