Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{AdS_3\times S^3\times T^4}$

TL;DR

This paper explores the $AdS_3\times S^3\times T^4$ string theory at $k=1$, revealing new symmetries and an exact Wakimoto description, which shed light on the bulk-boundary correspondence and the role of covering maps.

Contribution

It introduces an exact Wakimoto formalism for the $k=1$ string and uncovers a local worldsheet symmetry $Q(z)$ that localizes the path integral to covering maps.

Findings

Emergence of a local worldsheet symmetry $Q(z)$ at $k=1$

Localization of the path integral to covering maps

Identification of a radial translation symmetry in $AdS_3$

Abstract

This paper considers a recently-proposed string theory on $AdS_3\times S^3\times T^4$ with one unit of NS-NS flux ($k=1$). We discuss interpretations of the target space, including connections to twistor geometry and a more conventional spacetime interpretation via the Wakimoto representation. We propose an alternative perspective on the role of the Wakimoto formalism in the $k=1$ string, for which no large radius limit is required by the inclusion of extra operator insertions in the path integral. This provides an exact Wakimoto description of the worldsheet CFT. We also discuss an additional local worldsheet symmetry, $Q(z)$, that emerges when $k=1$ and show that this symmetry plays an important role in the localisation of the path integral to a sum over covering maps. We demonstrate the emergence of a rigid worldsheet translation symmetry in the radial direction of the $AdS_3$, for which again the presence of $Q(z)$ is crucial. We conjecture that this radial symmetry plays a key role in understanding, in the case of the $k=1$ string, the encoding of the bulk physics on the two-dimensional boundary.