The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Understand

The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix).

• Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane.
• In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters.
• In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories.