Segmented strings coupled to a B-field

TL;DR

This paper explores segmented strings in AdS3 coupled to a B-field, revealing an interpolation between Nambu-Goto and WZW models, with a classical reduction to a Toda-type theory and a singular WZW point.

Contribution

It introduces a unified framework connecting Nambu-Goto and WZW models via a coupling parameter, and shows the classical theory reduces to a Toda-type system independent of this coupling.

Findings

Classical theory reduces to a Toda-type system

WZW point is a singular degeneracy in the model

Action is independent of coupling in terms of kink momentum vectors

Abstract

In this paper we study segmented strings in AdS$_3$ coupled to a background two-form whose field strength is proportional to the volume form. By changing the coupling, the theory interpolates between the Nambu-Goto string and the $SL(2)$ Wess-Zumino-Witten model. In terms of the kink momentum vectors, the action is independent of the coupling and the classical theory reduces to a single discrete-time Toda-type theory. The WZW model is a singular point in coupling space where the map into Toda variables degenerates.