On the Dynamics of finite-gap solutions in classical string theory

We study the dynamics of finite-gap solutions in classical string theory on Rx S^3. Each solution is characterised by a spectral curve, \Sigma, of genus gand a divisor, \gamma, of degree g on the curve. We present a completereconstruction of the general solution and identify the correspondingmoduli-space, M^(2g)_R, as a real symplectic manifold of dimension 2g. Thedynamics of the general solution is shown to be equivalent to a specificHamiltonian integrable system with phase-space M^(2g)_R. The resultingdescription resembles the free motion of a rigid string on the Jacobian torusJ(\Sigma). Interestingly, the canonically-normalised action variables of theintegrable system are identified with certain filling fractions which play animportant role in the context of the AdS/CFT correspondence.Comment: 64 Pages, 5 Figures; typos corrected and references adde