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<p>The one-loop correction to eleven-dimensional supergravity involves a cubically divergent term <i>t</i><sub>8</sub><i>t</i><sub>8</sub><i>R</i><sup>4</sup>, with four Riemann tensors. A similar term (with finite coefficient) has been argued to be present in the M-theory effective action. It is expected to reduce to a similar one-loop term present in the type IIA effective action. This has previously been verified in the NSNS sector at the 4-point level. Here we extend this result to couplings of NSNS and RR fields, which have been computed using the pure spinor formalism. In particular, we check all couplings of RR fields to the dilaton as well as all couplings involving the metric and RR three-form. Correcting some minor mistakes in the literature we find complete agreement. We also give a complete analysis of 4-point terms in eleven dimensions computed previously from superparticle amplitudes and present a very simple form for these.</p>

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One loop in D = 11 vs D = 10: 4-point check

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Aviral Aggarwal,
  • Subhroneel Chakrabarti,
  • Steven Weilong Hsia,
  • Ahmed Rakin Kamal,
  • Linus Wulff

摘要

The one-loop correction to eleven-dimensional supergravity involves a cubically divergent term t8t8R4, with four Riemann tensors. A similar term (with finite coefficient) has been argued to be present in the M-theory effective action. It is expected to reduce to a similar one-loop term present in the type IIA effective action. This has previously been verified in the NSNS sector at the 4-point level. Here we extend this result to couplings of NSNS and RR fields, which have been computed using the pure spinor formalism. In particular, we check all couplings of RR fields to the dilaton as well as all couplings involving the metric and RR three-form. Correcting some minor mistakes in the literature we find complete agreement. We also give a complete analysis of 4-point terms in eleven dimensions computed previously from superparticle amplitudes and present a very simple form for these.