Stringy Corrections to Heterotic SU(3)-Geometry

We analyse the α \,² α ′ 2 corrections to the supersymmetry algebra constructed by Bergshoeff–de Roo for heterotic compactifications on SU(3) SU ( 3 ) manifolds. The geometry is complex and conformally balanced. Starting from these supersymmetry constraints, we derive the equations of motions and find that the graviton equation contains an extraneous term which can be set to zero after gauge fixing. The curvature of the tangent bundle connection acquires a nonzero (0, 2) component and so does not satisfy the instanton equation, showing that the tangent bundle instanton condition does not persist beyond first order in α \, α ′ .