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

TL;DR

This work develops a world-sheet framework to study non-supersymmetric strings on AdS$_3$ backgrounds, focusing on tachyonic type 0B and tachyon-free Spin(16)$\times$Spin(16)$\rtimes\mathbb{Z}_2$ heterotic strings. By formulating a generic SL(2,$\mathbb{R}$) WZW description and reading spectra from refined partition functions, the authors identify tachyonic regions induced by non-trivial Wilson lines in the heterotic theory, and they map the low-energy content (dilaton, gravitons, gauge fields, and moduli) for AdS$_3\times S^3\times T^4$ and AdS$_3\times S^3\times S^3\times S^1$. They demonstrate that even tachyon-free heterotic constructions can become unstable in the presence of Wilson lines, providing general formulas to analyze the classical moduli space and highlighting the need for further one-loop mass calculations to assess perturbative versus non-perturbative stability. The results advance understanding of non-supersymmetric string dynamics in curved backgrounds and offer a pathway to exploring potential holographic stories for these theories.

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.

Figures (3)

• Figure 3.1: We display the dispersion relation $(E,s)$ for the discrete representations choosing for simplicity $h_{T^4}=q=\bar{q}=j'=0, w=-2,k=7$. The points in green describe the states appearing both in the type IIB and type 0B superstring, while the points in red correspond to the additional sector entering the type 0B superstring.
• Figure 4.1: We show the plot of the variables $\{a_1,a_2\}$ for the choice of the radius $R^2=\alpha' (1-(a_1^2+a_2^2)/2)$ and Wilson line $A=(a_1,0^7;a_2,0^7)$ at $k_s^1=k_s^2=3$ and $j_1=j_2=0$. The blue region corresponds to tachyon-free points, while the red one to the tachyonic region.
• Figure 4.2: We show the plot of the variables $\{a_1,a_2\}$ for the choice of the radius $R^2=\alpha' (1-(a_1^2+a_2^2)/2)$ and Wilson line $A=(a_1,0^7;a_2,0^7)$ at $k_s^1=k_s^2=10^6$ and $j_1=j_2=0$. The blue region corresponds to tachyon-free points, while the red one to the tachyonic region.