Deriving the $\text{AdS}_{3}/\text{CFT}_{2}$ Correspondence

Understand

It was recently argued that string theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with one unit ($k=1$) of NS-NS flux is exactly dual to the symmetric orbifold CFT ${\rm Sym}^N(\mathbb{T}^4)$.

• In this paper we show how to directly relate the $n$-point correlators of the two sides to one another.
• In particular, we argue that the correlators of the world-sheet theory are delta-function-localised in string moduli space to those configurations that allow for a holomorphic covering map of the $\text{S}^2$-boundary of $\text{AdS}_3$ by the world-sheet.
• This striking feature can be seen both from a careful Ward identity analysis, as well as from semi-classically exact AdS$_3$ solutions that are pinned to the boundary.