Open Strings in the SL(2,R) WZWN Model with Solution for a Rigidly Rotating String

TL;DR

This paper investigates open strings in the $SL(2,R)$ WZWN model, focusing on boundary conditions, classical solutions for rigid rotation, and deriving a generalized Regge relation that extends flat space results.

Contribution

It introduces a new field-dependent gluing condition for open strings in $AdS_3$, enabling solutions with constant energy and angular momentum, and derives a generalized Regge relation.

Findings

Boundary conditions incompatible with the variation principle are identified.

Open strings with constant energy and angular momentum are constructed.

A generalized Regge relation for $SL(2,R)$ is derived, extending Minkowski space results.

Abstract

Boundary conditions and gluing conditions for open strings and D-branes in the $SL(2,R)$ WZWN model, corresponding to $AdS_3$, are discussed. Some boundary conditions and gluing conditions previously considered in the literature are shown to be incompatible with the variation principle. We then consider open string boundary conditions corresponding to a certain {\it field-dependent} gluing condition. This allows us to consider open strings with constant energy and angular momentum. Classically, these open strings naturally generalize the open strings in flat Minkowski space. For rigidly rotating open strings, we show that the torsion leads to a bending and an unfolding. We also derive the $SL(2,R)$ Regge relation, which generalizes the linear Minkowski Regge relation. For "high" mass, it takes the form $L\approx \pm M/H$, where $H$ is the scale of the $SL(2,R)$ group manifold.