On a family of ${\alpha }^{\prime }$-corrected solutions of the Heterotic Superstring effective action

Abstract

We compute explicitly the first-order in ${\alpha }^{\prime }$ 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 4 dimensions upon dimensional reduction on ${\mathrm{T}}^6$. We show that some of the ${\alpha }^{\prime }$ corrections can be cancelled by introducing solitonic $\mathrm{SU}(2)\times \mathrm{SU}(2)$ Yang-Mills fields, and that this family of ${\alpha }^{\prime }$-corrected solutions is invariant under ${\alpha }^{\prime }$-corrected T-duality transformations. We study in detail the mechanism that allows us to compute explicitly these ${\alpha }^{\prime }$ corrections for the ansatz considered here, based on a generalization of the 't Hooft ansatz to hyperKähler spaces.

v2: typos corrected, references added