Stringy Corrections to Heterotic SU(3)-Geometry

We analyse the ${\alpha }^{\mathrm{\prime }2}$ 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 ${\alpha }^{\mathrm{\prime }}$-corrections can disrupt semi-classical intuition.