T-duality Constraints on Higher Derivatives Revisited

TL;DR

This paper investigates how T-duality constrains higher-derivative corrections in string theory, extending previous methods to arbitrary field variables and applying it to determine first-order ' corrections and insights into second-order corrections in double field theory.

Contribution

It introduces a generalized method to test T-duality constraints on string effective actions using arbitrary field variables, improving upon earlier approaches.

Findings

Uniquely determines first-order ' corrections up to trivial terms.

Extends T-duality analysis to arbitrary field variables.

Provides insights into second-order '^2 corrections in double field theory.

Abstract

We ask to what extent are the higher-derivative corrections of string theory constrained by T-duality. The seminal early work by Meissner tests T-duality by reduction to one dimension using a distinguished choice of field variables in which the bosonic string action takes a Gauss-Bonnet-type form. By analyzing all field redefinitions that may or may not be duality covariant and may or may not be gauge covariant we extend the procedure to test T-duality starting from an action expressed in arbitrary field variables. We illustrate the method by showing that it determines uniquely the first-order $\alpha'$ corrections of the bosonic string, up to terms that vanish in one dimension. We also use the method to glean information about the ${\cal O}(\alpha'^2)$ corrections in the double field theory with Green-Schwarz deformation.