Algebraic Curves for Factorized String Solutions

TL;DR

This paper introduces a method to construct algebraic curves for factorized string solutions in AdS/CFT, using a local approach that avoids monodromy matrices, applicable to various boundary conditions.

Contribution

It presents a novel local construction of algebraic curves for factorized string solutions, expanding the tools available for analyzing integrable string configurations.

Findings

Constructed algebraic curves for factorized solutions.

Method applicable to solutions with arbitrary boundary conditions.

Provided examples demonstrating the procedure's effectiveness.

Abstract

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. The procedure can be applied for string solutions with any boundary conditions. We study the properties of the curve and give several examples for the application of the procedure.