Double-soft limits of gluons and gravitons

  • Thomas Klose
  • Tristan McLoughlin
  • Dhritiman Nandan
  • Jan Plefka
  • Gabriele Travaglini
Open Access
Regular Article - Theoretical Physics


The double-soft limit of gluon and graviton amplitudes is studied in four dimensions at tree level. In general this limit is ambiguous and we introduce two natural ways of taking it: a consecutive double-soft limit where one particle is taken soft before the other and a simultaneous limit where both particles are taken soft uniformly. All limits yield universal factorisation formulae which we establish by BCFW recursion relations down to the subleading order in the soft momentum expansion. These formulae generalise the recently discussed subleading single-soft theorems. While both types of limits yield identical results at the leading order, differences appear at the subleading order. Finally, we discuss double-scalar emission in \( \mathcal{N}=4 \) super Yang-Mills theory. These results should be of use in establishing the algebraic structure of potential hidden symmetries in the quantum gravity and Yang-Mills S-matrix.


Scattering Amplitudes Gauge Symmetry Space-Time Symmetries Supersymmetric gauge theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Thomas Klose
    • 1
  • Tristan McLoughlin
    • 2
  • Dhritiman Nandan
    • 1
    • 5
  • Jan Plefka
    • 1
  • Gabriele Travaglini
    • 1
    • 3
    • 4
  1. 1.Institut für Physik und IRIS Adlershof, Humboldt-Universität zu BerlinBerlinGermany
  2. 2.School of MathematicsTrinity College DublinDublin 2Ireland
  3. 3.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonUnited Kingdom
  4. 4.Dipartimento di FisicaUniversità di Roma “Tor Vergata”RomaItaly
  5. 5.Institut für Mathematik und IRIS Adlershof, Humboldt-Universität zu BerliBerlinGermany

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