Dimensional reduction of the M-theory Chern-Simons term at order $\ell_p^6$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909893781356544 |
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| author | Garousi, Mohammad R. |
| author_facet | Garousi, Mohammad R. |
| contents | The dimensional reduction of M-theory couplings at order $\ell_p^6$ is known to produce one-loop $α'^3$ corrections in type IIA string theory. In this paper, we perform the Kaluza-Klein reduction of the M-theory Chern-Simons coupling $t_8ε_{11} A R^4$ at this order. By meticulously accounting for non-gauge-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 $t_8ε_{10} B R^4$ which is gauge invariant up to total derivatives, but also unveil a new set of gauge-invariant couplings involving RR and NS-NS 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 $α'$ corrections in six dimensions transform under S-duality into the dimensional reduction of the tree-level heterotic string Chern-Simons coupling $H_{μνα} Ω^{μνα}$ on $T^4$. This non-trivial agreement provides strong evidence for the correctness of both the M-theory Chern-Simons term and its reduction to type IIA. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensional reduction of the M-theory Chern-Simons term at order $\ell_p^6$ Garousi, Mohammad R. High Energy Physics - Theory The dimensional reduction of M-theory couplings at order $\ell_p^6$ is known to produce one-loop $α'^3$ corrections in type IIA string theory. In this paper, we perform the Kaluza-Klein reduction of the M-theory Chern-Simons coupling $t_8ε_{11} A R^4$ at this order. By meticulously accounting for non-gauge-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 $t_8ε_{10} B R^4$ which is gauge invariant up to total derivatives, but also unveil a new set of gauge-invariant couplings involving RR and NS-NS 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 $α'$ corrections in six dimensions transform under S-duality into the dimensional reduction of the tree-level heterotic string Chern-Simons coupling $H_{μνα} Ω^{μνα}$ on $T^4$. This non-trivial agreement provides strong evidence for the correctness of both the M-theory Chern-Simons term and its reduction to type IIA. |
| title | Dimensional reduction of the M-theory Chern-Simons term at order $\ell_p^6$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.13726 |