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

Nick Dorey·Benoit Vicedo
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Abstract

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, Σ, of genus g and a divisor, γ, 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(Σ). 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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Nick Dorey, Benoit Vicedo. 2006-05-08. On the Dynamics of Finite-Gap Solutions in Classical String Theory. https://doi.org/10.1088/1126-6708%2F2006%2F07%2F014

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