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

TL;DR

This paper analyzes the dynamics of finite-gap solutions in classical string theory on R x S^3, revealing their integrable structure, moduli space, and connection to the AdS/CFT correspondence through action variables.

Contribution

It provides a complete reconstruction of finite-gap solutions, characterizes their moduli space as a symplectic manifold, and links their dynamics to a Hamiltonian integrable system.

Findings

Finite-gap solutions are characterized by a spectral curve and divisor.

The moduli space is a real symplectic manifold of dimension 2g.

Action variables correspond to filling fractions relevant in AdS/CFT.

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, \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.