The S-matrix Bootstrap III: Higher Dimensional Amplitudes

Authors:
  • MPMiguel F. Paulos
    Miguel F. Paulos
  • JPJoao Penedones
    Joao Penedones
  • JTJonathan Toledo
    Jonathan Toledo
  • BRBalt C. van Rees
    Balt C. van Rees
  • PVPedro Vieira
    Pedro Vieira
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Abstract
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. In the cases where our results can be compared with the older S-matrix literature they are in excellent agreement. We also extremize a cubic coupling in 2+1 dimensions which we can directly compare to a universal bound for a QFT in AdS. This paper generalizes our previous 1+1 dimensional results of arXiv:1607.06109 and arXiv:1607.06110.