Relativistic Calogero-Moser model as gauged WZW theory

Integrable deformation of the Calogero-Moser system is examined in the framework of the topological G/G Wess-Zumino-Witten model. It is shown that in the Hamiltonian approach the gauged WZW theory has a Hilbert space, which contains the one of the Ruijsenaars model. The latter can be described with the help of Verlinde algebra. Moreover, the evolution operator in the quantum mechanical problem has an interpretation in terms of the path integral in G/G theory with inserted Wilson line. We compute a partition function of the model using techniques from Chem-Simons theory, in particular, some surgeries of simple threefolds.