Tilting space of boundary conformal field theories

In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out examples in the case of free fields of spin zero and one-half. These results give a simple illustration of the salient features of conformal manifolds while generalizing to interacting and more intricate setups. Our work was inspired by Drukker et al. [Phys. Rev. Lett. 129, 201603 (2022)].