Quantum integrability in two-dimensional systems with boundary

In this letter we consider affine Toda systems defined on the half-plane and study the issue of quantum integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation at the quantum level. We compute corrections to the classical conservation laws in specific examples. We find that, except for the sinh-Gordon model, the existence of quantum conserved currents requires a finite renormalization of the boundary potential.