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

TL;DR

This paper explicitly computes first-order $oldsymbol{ extit{ extalpha'}}$ corrections to a family of solutions in heterotic superstring theory, revealing how certain corrections can be canceled and how the solutions behave under T-duality.

Contribution

It provides explicit $ extit{ extalpha'}$ corrections for heterotic string solutions with solitonic and black hole features, and demonstrates invariance under corrected T-duality.

Findings

Some $ extit{ extalpha'}$ corrections are cancelable with Yang-Mills fields.

The solutions are invariant under $ extit{ extalpha'}$-corrected T-duality.

Explicit correction formulas are derived using a generalized 't Hooft ansatz.

Abstract

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.