Geometric modular action for disjoint intervals and boundary conformal field theory

In suitable states, the modular group of local algebras associated with unions of disjoint intervals in chiral conformal quantum field theory acts geometrically. We translate this result into the setting of boundary conformal QFT and interpret it as a relation between temperature and acceleration. We also discuss aspects ("mixing" and "charge splitting") of geometric modular action for unions of disjoint intervals in the vacuum state.