Bootstrapping 2d $\phi^4$ Theory with Hamiltonian Truncation Data

Understand

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at $s>0$ in the 2d $\phi^4$ theory.

• We use the form factor of the stress tensor at $s\le 0$ and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up.
• The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime.
• We independently construct the "pure" S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the "staircase model" saturate these bounds.