# The Odd story of $\alpha'$-corrections

## TL;DR

This paper develops an extended Double Field Theory incorporating all first-order '-corrections, ensuring T-duality and gauge invariance, and unifies duality-constrained interactions in various gravity theories.

## Contribution

It introduces a gauged '-deformed DFT framework that includes all first-order '-corrections and extends previous models to generic (gauged/super)gravity theories.

## Key findings

- Includes all first '-corrections of string effective actions.
- Provides a unified framework for duality-constrained interactions.
- Ensures T-duality and gauge invariance in extended DFT.

## Abstract

The $\alpha'$-deformed frame-like Double Field Theory (DFT) is a T-duality and gauge invariant extension of DFT in which generalized Green-Schwarz transformations provide a gauge principle that fixes the higher-derivative corrections. It includes all the first order $\alpha'$-corrections of the bosonic and heterotic string low energy effective actions and of the Hohm-Siegel-Zwiebach $\alpha'$-geometry. Here we gauge this theory and parameterize it in terms of a frame, a two-form, a dilaton, gauge vectors and scalar fields. This leads to a unified framework that extends the previous construction by including all duality constrained interactions in generic (gauged/super)gravity effective field theories in arbitrary number of dimensions, to first order in $\alpha'$.