Stringy Corrections to Heterotic SU(3)-Geometry

We analyse the $\alpha'^2$ corrections to the supersymmetry algebra constructed by Bergshoeff--de Roo for heterotic compactifications on SU(3) manifolds. The geometry is complex and conformally balanced. We find an integrability condition for solutions related to the graviton equation of motion together with a correction that is pure gauge. We derive the same condition independently from hermitian geometry. The curvature of the tangent bundle connection acquires a nonzero (0,2) component and thus is not an instanton, illustrating how $\alpha'$-corrections can disrupt semi-classical intuition.