Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions

TL;DR

This paper reveals that certain classical Wilson loop solutions with trivial monodromy can still be described by algebraic curves, expanding the understanding of integrability in AdS/CFT correspondence.

Contribution

It demonstrates how Wilson loop minimal surfaces with trivial monodromy are represented by algebraic curves and connects correlation functions to this framework.

Findings

Wilson loop solutions with trivial monodromy are described by algebraic curves

Correlation functions of Wilson loops fit into the algebraic curve framework

Identifies differences between solutions with identical monodromy

Abstract

The algebraic curve (finite-gap) classification of rotating string solutions was very important in the development of integrability through comparison with analogous structures at weak coupling. The classification was based on the analysis of monodromy around the closed string cylinder. In this paper we show that certain classical Wilson loop minimal surfaces corresponding to the null cusp and qqbar potential with trivial monodromy can, nevertheless, be described by appropriate algebraic curves. We also show how a correlation function of a circular Wilson loop with a local operator fits into this framework. The latter solution has identical monodromy to the pointlike BMN string and yet is significantly different.