Gauged nonlinear sigma model and boundary diffeomorphism algebra

We consider Chern-Simons gauged nonlinear sigma model with boundary which has a manifest bulk diffeomorphism invariance. We find that the Gaussʹs law can be solved explicitly when the nonlinear sigma model is defined on the Hermitian symmetric space, and the original bulk theory completely reduces to a boundary nonlinear sigma model with the target space of Hermitian symmetric space. We also study the symplectic structure, compute the diffeomorphism algebra on the boundary, and find an (enlarged) Virasoro algebra with classical central term.