Tensionless String Spectra on ${\rm AdS}_3$

TL;DR

This paper analyzes the superstring spectrum on AdS3 backgrounds with pure NS-NS flux at minimal radius, revealing a match with free symmetric product orbifold spectra and proposing a world-sheet theory at k=1.

Contribution

It demonstrates a precise correspondence between tensionless string spectra on AdS3 and symmetric orbifold CFTs, including a concrete proposal for the world-sheet theory at minimal radius.

Findings

Identification of physical states matching orbifold spectra

Proposal of world-sheet theory at k=1

Implications for tensionless string theories

Abstract

The spectrum of superstrings on ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{M}_4$ with pure NS-NS flux is analysed for the background where the radius of the AdS space takes the minimal value $(k=1)$. Both for $\mathbb{M}_4={\rm S}^3 \times {\rm S}^1$ and $\mathbb{M}_4 = \mathbb{T}^4$ we show that there is a special set of physical states, coming from the bottom of the spectrally flowed continuous representations, which agree in precise detail with the single particle spectrum of a free symmetric product orbifold. For the case of ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ this relies on making sense of the world-sheet theory at $k=1$, for which we make a concrete proposal. We also comment on the implications of this striking result.