Spacetime dilaton in ${\rm AdS}_3\times X$ holography

TL;DR

This paper constructs DDF operators in ${ m AdS}_3\times X$ string theory with NSNS flux, providing evidence for a dual deformed symmetric orbifold CFT with a linear dilaton component, and implying the existence of a consistent background for generic $X$.

Contribution

It constructs DDF operators related to the spacetime linear dilaton, supporting the dual CFT conjecture and indicating the presence of a linear dilaton in generic backgrounds.

Findings

DDF operators for the spacetime linear dilaton are constructed.

Evidence supports the dual CFT as a deformed symmetric orbifold.

The existence of a linear dilaton background for generic $X$ is implied.

Abstract

We study the spectrum generating operators (DDF operators) for bosonic strings and superstrings in ${\rm AdS}_3\times X$ with pure, $\textit{generic}$ NSNS flux. The dual CFT is conjectured to be a deformed symmetric orbifold of $\mathbb{R}_{\widetilde{Q}}\times X$, where $\mathbb{R}_{\widetilde{Q}}$ denotes a linear dilaton theory with slope $\widetilde{Q}$. In this paper, we construct DDF operators corresponding to the spacetime linear dilaton field in the limit where the worldsheet theory becomes free. The DDF operator gives another evidence supporting the proposed dual CFT. Furthermore, the DDF operator is constructed purely from the $\rm AdS_3$ fields and thus, strongly implies the existence of $\mathbb{R}_{\widetilde{Q}}$ for generic $X$ that defines a consistent background.