The S-matrix Bootstrap IV: Multiple Amplitudes

Understand

We explore the space of consistent three-particle couplings in $\mathbb Z_2$-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 [arXiv:1607.06110] 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 [arXiv:1607.06109].
• 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 $\mathbb Z_2$ symmetry, e.g., the three-state Potts and tricritical Ising field theories.