Reflection factors and exact g-functions for purely elastic scattering theories

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.