Conformal Boundary Conditions in K-Matrix Luttinger Liquids

We investigate the (0+1)-dimensional conformal boundaries and defects in K-matrix Luttinger liquids, which could be realized in either (1+1)-dimensional systems with Dirac fermions, or edges of abelian topological quantum field theories. We derive general formulas for the boundary/defect central charge and the total ground state degeneracy. The connections to symmetric mass generation and SPT phases will be made. We also point out various other applications of the formulas.