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

TL;DR

We investigate the tensionless limit of superstrings on AdS3 with pure NS-NS flux at the minimal radius k=1. A distinguished subsector formed by the lowest states of spectrally flowed continuous representations reproduces the single-particle spectrum of a symmetric product orbifold, for both AdS3xS3xS3xS1 and AdS3xS3xT4. The authors develop a worldsheet description at k=1 and propose a symplectic-boson construction to render the T4 case well-defined, finding a matching with the symmetric orbifold of four bosons and four fermions. The results point to a universal tensionless structure governed by the Higher Spin Square, constraining the full spectrum beyond massless states and suggesting deep links between NS-NS backgrounds and symmetric orbifold CFTs.

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.