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

Geometries with twisted spheres and non-abelian T-dualities