Dimensional reduction of the M-theory Chern-Simons term at order ℓ_p⁶

2025/09/17 by Garousi, Mohammad R.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2509.13726

Abstract

The dimensional reduction of M-theory couplings at order ℓ_p⁶ 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 t₈ε₁₁ A R⁴ 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 t₈ε₁₀ B R⁴ 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 T⁴. This non-trivial agreement provides strong evidence for the correctness of both the M-theory Chern-Simons term and its reduction to type IIA.

Citations

• Type IIB at eight derivatives: Five-Point Axio-Dilaton Couplings
• One loop in D=11 vs D=10: 4-point check

Related

• The emergence of inherently 9-dimensional one-loop effective action from T-duality
• One-loop Chern-Simons terms in five dimensions
• Type IIA supergravity at one loop: α'³ terms in the metric-dilaton-RR one-form sector
• Quantum corrections to N=2 Chern-Simons theories with flavor and their AdS4 duals
• Effective action of heterotic string theory at order α'²