Boundary reflection matrices of massive ${\varphi }_{1,3}$-perturbed unitary minimal models

Abstract

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 ${\varphi }_{1,3}$ 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.

Latex, 52 pages, 13 figures, v2: clarified the notion of boundary subsets and added an Appendix on the definition of ABF lattice models

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