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.
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Garousi, M.R. Effective action of heterotic string theory at order α′2. J. High Energ. Phys. 2023, 20 (2023). https://doi.org/10.1007/JHEP09(2023)020
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DOI: https://doi.org/10.1007/JHEP09(2023)020