Supersymmetry, T-duality and Heterotic $\alpha'$-corrections

TL;DR

This paper constructs the first order ' corrections to heterotic string effective action using a T-duality covariant supergravity framework, incorporating supersymmetry and Green-Schwarz mechanism modifications.

Contribution

It introduces an exact, T-duality symmetric formulation of heterotic ' corrections, including a supersymmetric Green-Schwarz mechanism and deformations of supersymmetry transformations.

Findings

Derived the ' corrected effective action with four-derivative terms.

Established a supersymmetric, T-duality covariant Green-Schwarz mechanism.

Computed deformations of supersymmetry algebra coefficients.

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 ${\cal N}=1$ supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order $\alpha'$-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.