Heterotic string from a higher dimensional perspective

TL;DR

This paper demonstrates that the heterotic string effective action and supersymmetry conditions in ten dimensions can be equivalently described by a higher dimensional theory, revealing new insights into T-duality and solution generation.

Contribution

It establishes a higher dimensional framework for heterotic string theory, unifying the effective action, equations of motion, and supersymmetry conditions, and elucidates T-duality as a geometric exchange.

Findings

Higher dimensional action reproduces heterotic equations of motion.

Supersymmetry conditions correspond to higher dimensional geometric conditions.

Known solutions are related via a simple exchange of directions, suggesting new solutions.

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.