Integration of the SL(2,4$\mathbb R$) / U(1) gauged WZNW model with periodic boundary conditions

Gauged WZNW models are integrable conformal field theories. We integrate the classical SL(2, R )/U(1) theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson bracket structure by solving an initial state problem. The results differ from previous field-theoretic calculations due to zero-modes. For a future exact canonical quantization the physical fields are (non-locally) transformed onto canonical free fields