Algebraic Curves for Factorized String Solutions

Understand

We show how to construct an algebraic curve for factorized string solution in the context of the AdS/CFT correspondence.

• We define factorized solutions to be solutions where the flat-connection becomes independent of one of the worldsheet variables by a similarity transformation with a matrix $S$ satisfying $S^{-1}d S=const$.
• Using the factorization property we construct a well defined Lax operator and an associated algebraic curve.
• The construction procedure is local and does not require the introduction of a monodromy matrix.