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

Abstract

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

v2: typos corrected, references added