On a family of α′-corrected solutions of the Heterotic Superstring effective action

We compute explicitly the first-order in alpha' corrections to a family of solutions of the Heterotic Superstring effective action that describes fundamental strings with momentum along themselves, parallel to solitonic 5-branes with Kaluza-Klein monopoles (Gibbons-Hawking metrics) in their transverse space. These solutions correspond to 4 charge extremal black holes in alpha' dimensions upon dimensional reduction on T-6. We show that some of the at corrections can be cancelled by introducing solitonic SU(2) x SU(2) Yang-Mills fields, and that this family of alpha'-corrected solutions is invariant under alpha'-corrected T-duality transformations. We study in detail the mechanism that allows us to compute explicitly these alpha' corrections for the ansatz considered here, based on a generalization of the 't Hooft ansatz to hyperKahler spaces.