Heterotic string from a higher dimensional perspective

TL;DR

This work shows that the abelian bosonic heterotic string in ten dimensions, including α′ corrections, is equivalent to a higher-dimensional theory on tilde D = D + d_g when gauge fields are geometrized via a heterotic ansatz that fiberes U(1)^{d_g} over a base. By carefully scaling the higher-dimensional gauge connection as A^a_M ∼ √α′ 𝒜^a_M and fixing the base metric, the tilde D action, equations of motion, and Bianchi identity reproduce the heterotic results at order α′, effectively embedding gauge data into geometry. A corresponding set of tilde D SUSY conditions is shown to be equivalent to the standard heterotic SUSY constraints, including Hermitian Yang–Mills, offering a geometric interpretation of supersymmetric vacua and enabling trivial relations between Kähler and non-Kähler solutions via direction exchanges. The paper further develops a heterotic T-duality framework within this higher-dimensional setting, linking solutions through dualities that are not simply Buscher transformations and connecting to Generalized Complex Geometry, with potential non-geometric flux implications and avenues for new heterotic solutions. Overall, the work provides a duality-covariant, geometry-centric view of heterotic string theory with practical implications for solution generation and the study of flux vacua.

Abstract

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.