Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections

Abstract

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional $\mathcal{N}=1$ supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order ${\alpha }^{\prime }$-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

58 pages; v2: fixed typos, version to appear in JHEP