Effective action of heterotic string theory at order α′2

Abstract

Abstract Upon examining the effective action of the heterotic string theory at order α′2, an inconsistency between the Chern-Simons coupling Ω2 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 α′ 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 α′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 α′2.