On the Dynamics of Finite-Gap Solutions in Classical String Theory

Details On the Dynamics of Finite-Gap Solutions in Classical String Theory On the Dynamics of Finite-Gap Solutions in Classical String Theory

2006-01-25

arxiv.org/abs/hep-th/0601194v2

JHEP0607:014,2006

Physics

High Energy Physics

High Energy Physics - Theory

64 Pages, 5 Figures; typos corrected and references added

Scientific paper

10.1088/1126-6708/2006/07/014

We study the dynamics of finite-gap solutions in classical string theory on R x S^3. Each solution is characterised by a spectral curve, \Sigma, of genus g and a divisor, \gamma, of degree g on the curve. We present a complete reconstruction of the general solution and identify the corresponding moduli-space, M^(2g)_R, as a real symplectic manifold of dimension 2g. The dynamics of the general solution is shown to be equivalent to a specific Hamiltonian integrable system with phase-space M^(2g)_R. The resulting description resembles the free motion of a rigid string on the Jacobian torus J(\Sigma). Interestingly, the canonically-normalised action variables of the integrable system are identified with certain filling fractions which play an important role in the context of the AdS/CFT correspondence.

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