Non-supersymmetric strings on AdS$_3$: a world-sheet perspective

TL;DR

This paper investigates non-supersymmetric string theories on AdS$_3$ backgrounds using a world-sheet approach, revealing how Wilson lines induce tachyonic instabilities affecting vacuum stability.

Contribution

It provides a world-sheet description of non-supersymmetric strings on AdS$_3$ backgrounds and analyzes the impact of Wilson lines on the classical moduli space and stability.

Findings

Wilson lines cause tachyonic regions in moduli space

Explicit example on AdS$_3 imes S^3 imes S^3 imes S^1$ shows instability

General formulas for analyzing moduli space stability

Abstract

We explore the quantisation of the tachyonic type 0B superstring and the non-tachyonic $\text{Spin}(16) \times \text{Spin}(16) \rtimes \mathbb{Z}_2$ heterotic string on AdS$_3 \times S^3 \times T^4$ and AdS$_3 \times S^3 \times S^3 \times S^1$ backgrounds. Adapting the analysis for the supersymmetric and bosonic string theories to these set-ups, we provide a world-sheet description for a generic level of the $\text{SL}(2,\mathbb{R})$ WZW model, and we read the spectrum through the associated partition functions. Focusing on the low-energy theory, we show that the $\text{Spin}(16) \times \text{Spin}(16) \rtimes \mathbb{Z}_2$ heterotic string on both backgrounds accommodates non-trivial Wilson lines that are responsible for the appearance of tachyonic regions in the classical moduli space, hence jeopardising the stability of the vacuum. We show this with a concrete example on the AdS$_3 \times S^3 \times S^3 \times S^1$ space and provide general formulas for a systematic analysis of the classical moduli space.