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

Understand

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 4 dimensions upon dimensional reduction on $\mathrm{T}^{6}$.
• We show that some of the $\alpha'$ corrections can be cancelled by introducing solitonic $\mathrm{SU}(2)\times \mathrm{SU}(2)$ 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 hyperK\"ahler spaces.