Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

We consider the ground state of two species of one-dimensional critical free theories coupled together via a conformal interface. They have an internal U(1) global symmetry and we investigate the quantum fluctuations of the total charge on one side of the interface, giving analytical predictions for the full counting statistics, the charged moments of the reduced density matrix and the symmetry resolved Renyi entropies. Our approach is based on the relation between the geometry with the defect and the homogeneous one, and it provides a way to characterize the spectral properties of the correlation functions restricted to one of the two species. Our analytical predictions are tested numerically, finding a perfect agreement.