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Heterotic string from a higher dimensional perspective

The (abelian bosonic) heterotic string effective action, equations of motion and Bianchi identity at order alpha prime in ten dimensions, are shown to be equivalent to a higher dimensional action, its derived equations of motion and Bianchi identity. The two actions are the same up to the gauge fields: the latter are absorbed in the higher dimensional fields and geometry. This construction is inspired by heterotic T-duality, which becomes natural in this higher dimensional theory. We also prove the equivalence of the heterotic string supersymmetry conditions with higher dimensional geometric conditions. Finally, some known Kahler and non-Kahler heterotic solutions are shown to be trivially related from this higher dimensional perspective, via a simple exchange of directions. This exchange can be encoded in a heterotic T-duality, and it may also lead to new solutions.