Effective action of type II superstring theories at order $\alpha'^3$: NS-NS couplings

TL;DR

This paper determines the specific gauge invariant couplings at order α'^3 in type II superstring theories, ensuring T-duality invariance and consistency with previous S-matrix and sigma model results.

Contribution

It fixes all parameters of the NS-NS couplings at order α'^3 in type II superstrings using T-duality invariance, reducing the couplings to 445 non-zero structures.

Findings

445 non-zero couplings identified

Couplings consistent with S-matrix and sigma model results

Couplings organized into 15 structures

Abstract

Recently, it has been shown that the minimum number of gauge invariant couplings for $B$-field, metric and dilaton at order $\alpha'^3$ is 872. These couplings, in a particular scheme, appear in 55 different structures. In this paper, up to an overall factor, we fix all parameters in type II supertirng theories by requiring the reduction of the couplings on a circle to be invariant under T-duality transformations. We find that there are 445 non-zero couplings which appear in 15 different structures. The couplings are fully consistent with the partial couplings that have been found in the literature by the four-point S-matrix element and by the non-linear Sigma model methods.