A note on string solutions in AdS_3

TL;DR

This paper classifies classical open string solutions in AdS_3 using elliptic functions, identifying new solutions with null boundaries and degenerations, and extends the analysis by including the S^1 sector.

Contribution

It provides a systematic classification of elliptic function solutions in AdS_3 and explores their boundary structures, including null boundaries and degenerations.

Findings

Classified solutions satisfying reality and Virasoro conditions.

Identified solutions with six null boundaries, including collinear pairs.

Extended solutions by adding S^1 sector with four-cusp null boundary configurations.

Abstract

We systematically search for classical open string solutions in AdS_3 within the general class expressed by elliptic functions (i.e., the genus-one finite-gap solutions). By explicitly solving the reality and Virasoro conditions, we give a classification of the allowed solutions. When the elliptic modulus degenerates, we find a class of solutions with six null boundaries, among which two pairs are collinear. By adding the S^1 sector, we also find four-cusp solutions with null boundaries expressed by the elliptic functions.