Heterotic $\alpha$'-corrections in Double Field Theory

TL;DR

This paper extends Double Field Theory to incorporate first-order $oldsymbol{rac{ ext{alpha}}{ ext{prime}}}$ corrections for heterotic strings, enhancing the gauge symmetry framework and deriving corrected Buscher rules.

Contribution

It introduces a formalism that includes $oldsymbol{rac{ ext{alpha}}{ ext{prime}}}$ corrections into Double Field Theory for heterotic strings, with new flux formulations and corrected duality transformations.

Findings

Derived the Riemann curvature with torsion from generalized fluxes.

Reproduced all four-derivative terms, Bianchi identities, and equations of motion.

Obtained first-order $oldsymbol{rac{ ext{alpha}}{ ext{prime}}}$ corrections to heterotic Buscher rules.

Abstract

We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the $\alpha '$ expansion of the heterotic string low energy effective theory. The generalized tangent space and duality group are enhanced by $\alpha'$ corrections, and the gauge symmetries are generated by the usual (gauged) generalized Lie derivative in the extended space. The generalized frame receives derivative corrections through the spin connection with torsion, which is incorporated as a new degree of freedom in the extended bein. We compute the generalized fluxes and find the Riemann curvature tensor with torsion as one of their components. All the four-derivative terms of the action, Bianchi identities and equations of motion are reproduced. Using this formalism, we obtain the first order $\alpha'$ corrections to the heterotic Buscher rules. The relation of our results to alternative formulations in the literature is discussed and future research directions are outlined.