Abstract
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with a fixed mass spectrum. In special cases we identify interesting integrable theories saturating these bounds. Our analytic bounds match precisely with numerical bounds obtained in a companion paper where we consider massive QFT in an AdS box and study boundary correlators using the technology of the conformal bootstrap.
Highlights
With the appearance of quantum chromodynamics, this program lost part of its original motivation and sort of faded away in its original form, morphing into string theory
This induces conformal theories living at the AdS boundary which we can numerically study by means of the conformal bootstrap
An important hint arose from the numerics of the last section: for the simplest possible mass spectrum, we found that the optimal S-matrix — leading
Summary
Our main object of study will be the 2 → 2 S-matrix elements of a relativistic two dimensional quantum field theory. We normalize gj to be the residue in the invariant matrix element T which differs from S by the subtraction of the identity plus some simple Jacobians related to the normalization of delta functions in the connected versus disconnected components. This justifies the prefactors Jj in (2.3).. As we increase the coupling to m1 we expect this to generate an attractive force mediated by the particle m1 between the two external masses At some point, this force is such that new bound states are bound to show up, invalidating the spectrum we took as input.
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