Strings in extremal BTZ black holes

TL;DR

This paper analyzes the spectrum of bosonic closed strings in extremal BTZ black holes using a hyperbolic Wakimoto representation, revealing tachyonic modes in the twisted sector and exploring connections to null orbifolds.

Contribution

It introduces a novel vertex operator construction for string modes in extremal BTZ backgrounds and discusses the presence of tachyons and their localization.

Findings

Tachyons are present in the twisted sector but are not horizon-localized.

The vertex operator construction is based on a hyperbolic Wakimoto representation.

Connections to null orbifolds are explored in the zero cosmological constant limit.

Abstract

We study the spectrum of the worldsheet theory of the bosonic closed string in the massless and extremal rotating BTZ black holes. We use a hyperbolic Wakimoto representation of the SL(2,R) currents to construct vertex operators for the string modes on these backgrounds. We argue that there are tachyons in the twisted sector, but these are not localised near the horizon. We study the relation to the null orbifold in the limit of vanishing cosmological constant. We also discuss the problem of extending this analysis to the supersymmetric case.