T-duality invariant effective actions at orders $ \alpha', \alpha'^2$

TL;DR

This paper derives T-duality invariant effective actions in string theory at orders ' and '^2, fixing couplings and corrections by imposing duality constraints, and suggests a general method for higher orders.

Contribution

It provides a systematic way to determine covariant effective actions consistent with T-duality at ' and '^2, up to field redefinitions and overall factors.

Findings

T-duality constrains effective actions at ' and '^2.

Effective actions are fixed up to field redefinitions and overall factors.

The approach can be extended to higher ' orders.

Abstract

We use compatibility of the $D$-dimensional effective actions for diagonal metric and for dilaton with the T-duality when theory is compactified on a circle, to find the the $D$-dimensional couplings of curvatures and dilaton as well as the higher derivative corrections to the $(D-1)$-dimensional Buscher rules at orders $ \alpha' $ and $\alpha'^2$. We observe that the T-duality constraint on the effective actions fixes the covariant effective actions at each order of $\alpha'$ up to field redefinitions and up to an overall factor. Inspired by these results, we speculate that the $D$-dimensional effective actions at any order of $\alpha'$ must be consistent with the standard Buscher rules provided that one uses covariant field redefinitions in the corresponding reduced $(D-1)$-dimensional effective actions. This constraint may be used to find effective actions at all higher orders of $\alpha'$.