On type II string theory on $AdS_3\times S^3\times T^4$ and symmetric orbifolds

TL;DR

This paper explores the duality between type II string theory on $AdS_3\times S^3\times T^4$ and symmetric orbifold conformal field theories, detailing the emergence of string genus expansion and strong coupling limits within the orbifold framework.

Contribution

It provides a detailed analysis of the string duality, showing how the genus expansion arises and explaining the strong coupling behavior in the symmetric orbifold description.

Findings

String genus expansion is derived to all orders in the orbifold CFT.

The strong coupling limit corresponds to a non-perturbative regime without a weakly coupled R-R dual.

The dual CFT includes an extra decoupled $T^4$ factor and marginal deformations relate different flux values.

Abstract

We discuss in detail the $1+1$-dimensional superconformal field theory dual to type II string theory on $AdS_3\times S^3\times T^4$, emphasizing the string theoretic aspects of this duality. For one unit of NS-NS 5-brane flux ($Q_5=1$), this string theory has been suggested to be dual to a grand-canonical ensemble of $T^{4N}/S_N$ free symmetric orbifold CFTs. We show how the string genus expansion emerges to all orders for the free orbifold grand-canonical correlation functions. We also discuss how the strong coupling limit of the NS-NS string theory arises (even at large $N$) in the free orbifold description, and argue why this limit does not have a weakly coupled R-R description. The dual CFT includes (for all values of $Q_5$) an extra $T^4$ factor that is decoupled from perturbative string theory. We discuss the exactly marginal deformations that relate the different values of $Q_5$, including the precise $J{\bar J}$ deformations mixing this extra $T^4$ with the symmetric orbifold.