A twistor-sphere of generalized Kahler potentials on hyperkahler manifolds

Abstract

We consider generalized Kahler structures (g,J_+,J_-) on a hyperkahler manifold (M,g,I,J,K), where we use the twistor space of M to choose J_+ and J_-. Relating semi-chiral to arctic superfields, we can determine the generalized Kahler potential for hyperkahler manifolds whose description in projective superspace is known. This is used to determine an S2-family of generalized Kahler potentials for Euclidean space and for the Eguchi-Hanson geometry.