Wound and Rotating Strings in AdS_5 x S^5

TL;DR

This paper derives a gauge-fixed Hamiltonian for wound and rotating strings in AdS_5 x S^5, analyzing their energy-angular momentum relations and exploring solutions with different angular orientations.

Contribution

It introduces a non-diagonal gauge approach to derive a square-root Hamiltonian and constructs explicit wound string solutions with rotation in AdS_5 x S^5.

Findings

Energy-angular momentum relation becomes linear at large angular momentum.

Constructed explicit wound string solutions with rotation in the same and different angular directions.

Compared small angular momentum limit with strong coupling gauge theory results.

Abstract

By using the non-diagonal uniform gauge for the Nambu-Goto string action we derive a gauge-fixed Hamiltonian of a square-root form for the closed string in AdS_5 x S^5 which is wound and rotating in an angular direction in S^5. From the Nambu-Goto string action using a non-diagonal gauge we construct a solution describing a wound string which rotates in the same angular direction as the winding direction. The relation between energy and angular momentum of the string solution is characterized by the winding number and the bending number, and becomes linear in the large angular momentum limit. The small angular momentum limit is compared with the strong coupling limit of the gauge-fixed Hamiltonian. We analyze a wound string solution which is rotating in the different angular direction from the winding direction.