Higher-derivative corrections to small black rings

We compute the first-order ${\alpha }^{\mathrm{\prime }}$-corrections to a general family of supersymmetric heterotic backgrounds which describes a rotating superposition of a fundamental string and a momentum wave. We focus on a particular solution within this family that gives raise, upon dimensional reduction to five dimensions, to a black ring with two charges and one dipole that has a singular horizon with vanishing area in the supergravity approximation, better known as small black ring. We show that the singularity at the horizon persists even after the first-order ${\alpha }^{\mathrm{\prime }}$-corrections have been taken into account. This implies, contrary to what has been argued in the literature, that higher-derivative corrections do not resolve the singular horizon of the 5-dimensional small black ring, at least at first-order in ${\alpha }^{\mathrm{\prime }}$.