Journal of High Energy Physics

, 2019:76 | Cite as

The S-matrix bootstrap IV: multiple amplitudes

  • Alexandre HomrichEmail author
  • João Penedones
  • Jonathan Toledo
  • Balt C. van Rees
  • Pedro Vieira
Open Access
Regular Article - Theoretical Physics


We explore the space of consistent three-particle couplings in ℤ2-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the two-to-two scattering amplitudes and extends the techniques of [2] to a multi-amplitude setup. Our second approach is based on placing QFTs in AdS to get upper bounds on couplings with the numerical conformal bootstrap, and is a multi-correlator version of [1]. The space of allowed couplings that we carve out is rich in features, some of which we can link to amplitudes in integrable theories with a ℤ2 symmetry, e.g., the three-state Potts and tricritical Ising field theories. Along a specific line our maximal coupling agrees with that of a new exact S-matrix that corresponds to an elliptic deformation of the supersymmetric Sine-Gordon model which preserves unitarity and solves the Yang-Baxter equation.


Field Theories in Lower Dimensions Integrable Field Theories Scattering Amplitudes 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.ICTP South American Institute for Fundamental Research, IFT-UNESPSão PauloBrazil
  3. 3.Fields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  4. 4.Centre for Particle Theory, Department of Mathematical SciencesDurham UniversityDurhamU.K.

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