The S-matrix Bootstrap III: Higher Dimensional Amplitudes

TL;DR

This paper extends the S-matrix bootstrap approach to higher dimensions, deriving bounds on scattering amplitudes in 3+1 and 2+1 dimensions using fundamental principles like crossing symmetry, analyticity, and unitarity.

Contribution

It generalizes previous 1+1 dimensional results to 3+1 and 2+1 dimensions, providing new bounds on couplings and scattering lengths in higher-dimensional quantum field theories.

Findings

Results agree with older S-matrix literature where comparisons are possible.

Derived bounds on cubic and quartic couplings in 3+1 dimensions.

Established a universal bound for a QFT in AdS in 2+1 dimensions.

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.