We discuss reflection factors for purely elastic scattering theories and relate them to perturbations of specific conformal boundary conditions, using recent results on exact off-critical g-functions. For the non-unitary cases, we support our conjectures using a relationship with quantum group reductions of the sine-Gordon model. Our results imply the existence of a variety of new flows between conformal boundary conditions, some of them driven by boundary-changing operators.

We study a three-parameter family of PT -symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordon block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender-Dunne polynomials, and gives a new insight into a phase transition to infinitely-many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly-solvable limit, the inhomogeneous complex square well, is also identified. 1 p.e.dorey@durham.ac.uk 2 t.c.dunning@kent.ac.uk 3 AnnaLishman@dunelm.org.uk 4 tateo@to.infn.it * Note, a propagating typo in [1] and [8] resulted in the factor of (−1) k multiplying kα/2 in the exponent of ω being omitted from the definition of y k given in those papers. None of the other formulae in [1,8] are affected.