The Worldsheet Dual of the Symmetric Product CFT (1812.01007v1)

Abstract: Superstring theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with the smallest amount of NS-NS flux (`$k=1$') is shown to be dual to the spacetime CFT given by the large $N$ limit of the free symmetric product orbifold $\mathrm{Sym}^N(\mathbb{T}^4)$. To define the worldsheet theory at $k=1$, we employ the hybrid formalism in which the ${\rm AdS}_3\times {\rm S}^3$ part is described by the $\mathfrak{psu}(1,1|2)_1$ WZW model (which is well defined). Unlike the case for $k\geq2$, it turns out that the string spectrum at $k=1$ does {\it not} exhibit the long string continuum, and perfectly matches with the large $N$ limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.

• The paper demonstrates that at k=1, the worldsheet theory lacks a long string continuum, matching the symmetric orbifold CFT spectrum.
• The authors employ the hybrid formalism to construct a well-defined framework that bypasses limitations of the conventional RNS approach.
• Fusion rules analysis confirms the duality by aligning worldsheet-derived results with those from the symmetric orbifold theory.

Overview of "The Worldsheet Dual of the Symmetric Product CFT"

This paper examines the intricacies of the AdS/CFT correspondence within the specific context of string theory on $\text{AdS}_3 \times \text{S}^3 \times \text{T}^4$ with minimal $\text{NS-NS}$ flux ($k=1$). The authors, Eberhardt, Gaberdiel, and Gopakumar, utilize a novel hybrid formalism to eschew the complications often associated with the RNS formalism at lower values of $k$, which is not well-defined for $k < 2$. Their main result is the demonstration that this string setup is dual to the large $N$ limit of the free symmetric product orbifold CFT, $\text{Sym}^N(T^4)$.

Key Contributions:

• Worldsheet Theory without Long String Continuum: The authors show that at $k=1$, the worldsheet theory does not feature a long string continuum, contrasting the behavior observed for higher levels of flux ($k \geq 2$). This absence simplifies the string spectrum, showing perfect agreement with the symmetric orbifold CFT in the large $N$ limit.
• Hybrid Formalism: The paper utilizes the hybrid formalism crafted by Berkovits, Vafa, and Witten, where the $\text{AdS} \times \text{S}$ sector is depicted through the $\text{PSU}(1,1|2)$ WZW model, while $T^4$ is treated as topologically twisted. This approach provides a well-defined framework even at $k=1$, overcoming the limitations of traditional formalisms.
• Fusion Rules Consistency: The authors further validate their proposal by demonstrating that the fusion rules derived from the worldsheet perspective align with those expected from the symmetric orbifold theory. This provides further backing for the duality claim and suggests a coherent underlying structure to the worldsheet theory in this limit.

Practical and Theoretical Implications:

The tractable description presented offers fresh insights into tensionless limits of string backgrounds and their potential dual CFTs. This work underscores the utility of supergroup models in accessing these exotic limits and provides a mechanism to rectify discrepancies between worldsheet descriptions and their respective dual spacetime CFTs.

Future Directions:

Anticipated advances could include a deeper exploration of stringy symmetries in such low tension regimes, as alluded to in ongoing discussions of higher spin symmetries and the Higher Spin Square. Future work may focus on the completion of comparatives studies involving non-BPS operator correlators, extending the analysis to other AdS backgrounds with maximal supersymmetry, and more detailed investigations into the connections between topological strings and free CFTs.

In summary, this paper makes a substantial contribution to understanding the AdS/CFT correspondence by elucidating a novel duality at $k=1$ using hybrid formulation techniques, aligning theoretical predictions with observable fusion rules, and paving the way for further developments in string theory and related explorations.