Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve

Understand

We review the spectral curve for the classical string in AdS5xS5.

• Classical integrability of the AdS5xS5 string implies the existence of a flat connection, whose monodromies generate an infinite set of conserved charges.
• The spectral curve is constructed out of the quasi-momenta, which are eigenvalues of the monodromy matrix, and each finite-gap classical solution can be characterized in terms of such a curve.
• This provides a concise and powerful description of the classical solution space.