Relative entropy of conformal interfaces, boundary states, and the applications to Chern-Simons theories

Relative entropy is a measure to distinguish two quantum states. In this work, we study the relative entropy for a 1+1 dimensional CFT with different conformal interfaces/defects and conformal boundary conditions. By using relative entropy, we can extract the universal data of conformal interfaces/defects and conformal boundary states. In addition, we apply our methods to 2+1 dimensional Chern-Simons theories. It is found that the results are sensitive to whether the theory is Abelian or non-Abelian, and can be used to detect topological data without UV divergence.