The B-field soft theorem and its unification with the graviton and dilaton

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


In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton’s soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.


Bosonic Strings Scattering Amplitudes Superstrings and Heterotic Strings 


Open Access

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Copyright information

© The Author(s) 2017

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 NapoliComplesso Universitario di Monte S. Angelo ed. 6NapoliItaly
  4. 4.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutPotsdamGermany

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