Multiloop Soft Theorem for Gravitons and Dilatons in the Bosonic String

Abstract

We construct, in the closed bosonic string, the multiloop amplitude involving $N$ tachyons and one massless particle with $26-D$ compactified directions, and we show that at least for $D>4$, the soft behaviors of the graviton and dilaton satisfy the same soft theorems as at the tree level, up to one additional term at the subsubleading order, which can only contribute to the dilaton soft behavior and which we show is zero at least at one loop. This is possible, since the infrared divergences due to the non-vanishing tachyon and dilaton tadpoles do not depend on the number of external particles and are therefore the same both in the amplitude with the soft particle and in the amplitude without the soft particle. Therefore this leaves unchanged the soft operator acting on the amplitude without the soft particle. The additional infrared divergence appearing for $D\le 4$ depend on the number of external legs and must be understood on their own.

arXiv comment20 p. + 23 p. appendices. New version to match the published version; new appendix (A) added and dependence on compactification radii clarified

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Cited by in corpus (8)

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• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
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• Soft Theorems from Compactification
• Soft factors from classical scattering on the Reissner-Nordström spacetime
• On the multiloop soft theorem of the dilaton in the bosonic string
• Soft-Theorems for Scalar Particles: The Dilatons Story