T-duality and $\alpha'$-corrections

TL;DR

This paper develops an $O(d,d)$ invariant framework for first-order $eta'$-corrections in string effective actions, unifying different string theories and clarifying duality symmetries and gauge transformations.

Contribution

It introduces a universal, duality-covariant formulation of $eta'$-corrections that interpolates between bosonic and heterotic string effective actions using a generalized Green-Schwarz mechanism.

Findings

Constructed an $O(d,d)$ invariant action with two free parameters.

Reproduces bosonic string effective action with $Z_2$-symmetry.

Derives heterotic string effective action via $Z_2$-parity-breaking.

Abstract

We construct an $O(d,d)$ invariant universal formulation of the first-order $\alpha'$-corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a $Z_2$-parity transformation that changes the sign of the two-form field. The $Z_2$-symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a $Z_2$-parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the four-derivative terms. We discuss the $O(d,d)$ structure of the theory and the (non-)covariance of the required field redefinitions.