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Multiloop soft theorem for gravitons and dilatons in the bosonic string

  • Paolo Di Vecchia
  • Raffaele Marotta
  • Matin MojazaEmail author
Open Access
Regular Article - Theoretical Physics

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 ≤ 4 depend on the number of external legs and must be understood on their own.

Keywords

Bosonic Strings Scattering Amplitudes 

Notes

Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Paolo Di Vecchia
    • 1
    • 2
  • Raffaele Marotta
    • 3
  • Matin Mojaza
    • 4
    Email author
  1. 1.The Niels Bohr InstituteUniversity of CopenhagenCopenhagen ØDenmark
  2. 2.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden
  3. 3.Istituto Nazionale di Fisica Nucleare, Sezione di NapoliNapoliItaly
  4. 4.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutPotsdamGermany

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