The S-matrix bootstrap. Part III: higher dimensional amplitudes
Miguel Paulos (Theoretical Physics Department, CERN, Geneva, Switzerland); Joao Penedones (Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland); Jonathan Toledo (Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland); Balt Rees (Centre for Particle Theory, Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham, DH1 3LE, U.K.); Pedro Vieira (ICTP South American Institute for Fundamental Research, IFT-UNESP, São Paulo, SP, 01440-070, Brazil, Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada)
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 [1] and [2].
