# Four-derivative couplings via T-duality constraint

## TL;DR

This paper investigates how T-duality invariance constrains the form of the effective action and higher derivative corrections in string theory compactified on a circle, providing explicit calculations at order α' and fixing the corrections up to an overall factor.

## Contribution

It demonstrates that T-duality constraints can determine the effective action and higher derivative corrections at order α' in string theory, including scheme dependence.

## Key findings

- T-duality invariance fixes the effective action and corrections up to an overall factor.
- Explicit calculations at order α' confirm the constraints.
- The results are valid in arbitrary schemes.

## Abstract

We examine the proposal that the dimensional reduction of the effective action of perturbative string theory on a circle, should be invariant under T-duality transformations. The T-duality transformations are the standard Buscher rules plus some higher covariant derivatives. By explicit calculations at order $\alpha'$ for metric, dilaton and B-field, we show that the T-duality constraint can fix both the effective action and the higher derivative corrections to the Buscher rules up to an overall factor. The corrections depend on the scheme that one uses for the effective action. We have found the effective action and its corresponding T-duality transformations in an arbitrary scheme.