Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5

TL;DR

This paper constructs algebraic curves for specific long string configurations in AdS5xS5 using the finite-gap method, revealing connections to null cusp Wilson loops and characterizing branch points via Virasoro constraints.

Contribution

It introduces a method to derive algebraic curves for long folded and circular winding strings in AdS5xS5, linking them to known Wilson loop configurations.

Findings

Long spiky string in AdS3 shares algebraic curve with null cusp Wilson loop.

Algebraic curve for circular winding string in AdS3xS1 is explicitly evaluated.

Virasoro constraint helps characterize the branch points of the algebraic curves.

Abstract

For the homogeneous configuration given by the long string limit of the folded string with a spin in AdS3 and a spin and a winding number in S1, we solve the auxiliary linear problem in the finite-gap method and construct the Lax operator to obtain an algebraic curve. We show that the long spiky string in AdS_3 has the same algebraic curve as the null cusp Wilson loop. The algebraic curve for the circular winding string in AdS3xS1 is evaluated. The Virasoro constraint is discussed to characterize the branch points of each curve.