Boundary reflection matrices of massive ϕ1,3-perturbed unitary minimal models

A bstract We propose explicit expressions for the boundary reflection matrices of the $${\mathcal{A}}_{m}+(r, s)$$ series of massive scattering theories, obtained by perturbing the $${\mathcal{A}}_{m}$$ unitary minimal models with ( r, s ) boundary conditions with both bulk and boundary ϕ 1 , 3 operators. We identify the vacua that live on the boundary with the allowed edges of the ( r, s ) conformal boundary conditions of the A m Andrews-Baxter-Forrester model. The boundary reflection matrices are then “direct sums” of certain pairs of A m− 1 Behrend-Pearce solutions of the boundary Yang-Baxter equation and are consistent with the boundary bootstrap and the recently-introduced crossing, as well as the Z 2 (height-reversal), Kac table and non-invertible symmetries.