Effective action of heterotic string theory at order $\alpha'^2$

TL;DR

This paper resolves an inconsistency in the heterotic string theory's effective action at order α'^2 by introducing new couplings and ensuring T-duality invariance, aligning with S-matrix results.

Contribution

It introduces 60 new geometrical couplings at order α'^2 and determines their coefficients to restore T-duality invariance, resolving previous inconsistencies.

Findings

Coefficients of Riemann cubed terms are zero, matching S-matrix results.

Successfully incorporates parity odd couplings at order α'^2.

Restores consistency between Chern-Simons coupling and T-duality.

Abstract

Upon examining the effective action of the heterotic string theory at order $\alpha'^2$, an inconsistency between the Chern-Simons coupling $\Omega^2$ and T-duality has been discovered. To address this issue, we introduce 60 parity-even independent geometrical couplings involving the $B$-field, metric, and dilation at the same order, each with arbitrary coefficients. To ensure the invariance of these couplings under T-duality, we consider the Miessner action for the couplings at order $\alpha'$ and rigorously determine the coefficients of the 60 couplings in terms of the Chern-Simons coupling. Notably, it is found that the coefficients of the Riemann cubed terms must be zero, which aligns with the results of S-matrix calculations. Additionally, the parity odd couplings at order $\alpha'^2$ are obtained through T-duality. Overall, our analysis successfully resolves the inconsistency between the Chern-Simons coupling and T-duality, providing a more comprehensive understanding of the behavior of the heterotic string theory at order $\alpha'^2$.