Effective $AdS_3/CFT_2$ (2501.09119v3)

Abstract: In arXiv:2109.00065, it was pointed out that superstring theory on $AdS_3$ with $(NS,NS)$ $B$-field background and $R_{AdS}/l_s=\sqrt k<1$ is dual to a symmetric product CFT deformed by an operator in the $\mathbb{Z}_2$ twisted sector. We generalize the analysis of arXiv:2109.00065 to $k>1$, and show that the resulting picture matches that discussed in the bosonic case in arXiv:2110.07535. We argue that in the critical case, $k=1$ hep-th/0503121, the $\mathbb{Z}_2$ twisted deformation remains non-trivial. This resolves some confusions in the literature.

• The paper extends the duality framework to the k≥1 regime with a deformed symmetric product CFT that effectively captures low-energy excitations.
• It reveals that modifications in spacetime modular invariance lead to significant implications for understanding BTZ black hole microstates.
• The authors analyze models such as AdS3 x S3 x T4 and AdS3 x S3 x S3 x S1, opening new avenues for exploring quantum gravity in three dimensions.

Effective AdS3/CFT2 Duality: A Critical Examination

This paper by Chakraborty, Giveon, and Kutasov extends and further elucidates the duality between superstring theory on AdS3 supported by a (NS, NS) B-field and certain two-dimensional conformal field theories (CFT2). Specifically, it addresses the complexities arising when the ratio of the AdS radius to the string length, $R_{\text{AdS}}/l_s = \sqrt{k}$, exceeds one, broadening the scope of previous work which primarily focused on the $k < 1$ regime.

In the $k < 1$ scenario, the dual CFT is a symmetric product of Seiberg-Witten (SW) long string theories, modified by a deformation in the $\mathbb{Z}_2$ twisted sector. This research presents a comprehensive continuation of this framework to $k \geq 1$, pointing out that the deformed symmetric product of SW CFT continues to be significant. The paper supports the hypothesis that in this domain, the theory efficiently accounts for low-energy excitations, despite the full-scale theory incorporating features that the symmetric product cannot completely describe, such as BTZ black holes.

Key Results and Theoretical Implications

The extension to $k > 1$ is nontrivial due to the modified landscape of the string coupling and its implications on spacetime modular invariance. Chakraborty et al. argue that the spacetimes in the $k > 1$ regime, though not fully modular invariant due to asymptotic states resembling black holes, still retain an effective theory captured by a deformed symmetric product CFT. Notably, in the extreme case of $k = 1$, the Seiberg-Witten description remains valid in the UV but requires modifications in the infrared, an insight that resolves previous ambiguities in the literature.

The authors systematically explore prominent examples of such theories, including cases like AdS3 x S3 x T4 and AdS3 x S3 x S3 x S1, each illustrating unique implications of the deformation in their specific symmetric orbifold structures. These illustrative models emphasize the robustness of their theoretical extension beyond the bosonic strings and hint at its pertinence to fermionic strings, with or without explicit spacetime supersymmetry.

Future Directions and Speculative Conclusions

The insights gained in this paper propose several future research avenues. Firstly, resolving the complete nature of spacetime CFT beyond the description provided by symmetric products might illuminate more intricate properties of quantum gravity in three dimensions. Additionally, understanding the interplay of these theories with BTZ black hole microstates remains a compelling objective, particularly in light of the non-modular invariance in $k > 1$.

As advances in theoretical physics push the boundaries of quantum gravity and emergent phenomena within string theory contexts, the explorations set forth by Chakraborty et al. provide a solid foundation for probing deeper into the AdS/CFT correspondence. Moreover, extending such a framework to potentially more complex backgrounds, devoid of supersymmetry or with distinct compactified internal spaces, could unveil more profound aspects of duality and string dynamics on AdS3 manifolds.

This inquiry into the field of superstring theory on AdS3 spaces, intertwined with the enriched understanding of symmetric product CFTs, yields a strategic stepping stone toward deciphering the nuanced interfacial behaviors and dual relationships at the confluence of contemporary theoretical physics.