The dimensional reduction of M-theory couplings at order ${\ell }_p^6$ is known to produce one-loop ${\alpha }^{\prime 3}$ corrections in type IIA string theory. In this paper, we perform the Kaluza-Klein reduction of the M-theory Chern-Simons coupling $t_8{\epsilon }_{11}A{R}^4$ at this order. By meticulously accounting for nongauge-invariant total derivative terms, we derive the complete set of corresponding one-loop, gauge-invariant couplings in the type IIA effective action. Our results not only reproduce the standard Chern-Simons term $t_8{\epsilon }_{10}B{R}^4$—which is gauge invariant up to total derivatives—but also unveil a new set of gauge-invariant couplings involving Ramond-Ramond and Neveu-Schwarz–Neveu-Schwarz field strengths. To validate our findings, we test their consistency under string dualities. We dimensionally reduce the derived type IIA couplings on a K3 manifold and show that the resulting one-loop ${\alpha }^{\prime }$ corrections in six dimensions transform under S-duality into the dimensional reduction of the tree-level heterotic string Chern-Simons coupling $H_{\mu \nu \alpha }{\mathrm{\Omega }}^{\mu \nu \alpha }$ on $T^4$. This nontrivial agreement provides strong evidence for the correctness of both the M-theory Chern-Simons term and its reduction to type IIA.

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• M-theory
• String dualities
• Supergravity