Twisted holography on AdS$$_3 \times S^3 \times$$ K3 & the planar chiral algebra

Journal Article · 09 October 2024 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.17.4.109 · OSTI ID:2461629

Fernández, Víctor E.; Paquette, Natalie ; Williams, Brian

In this work, we revisit and elaborate on twisted holography for AdS _3 × S^3 × X ${}_3\times S^3\times X$ with X= T^4 $X=T^4$ , K3, with a particular focus on K3. We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the N → ∞ $N\to \infty$ , or planar, limit of the chiral algebra of the dual CFT. The resulting symmetries are strong enough to fix planar 2 and 3-point functions in the twisted theory or, equivalently, in a 1/4-BPS subsector of the original duality. This technique can in principle be used to compute corrections to the chiral algebra perturbatively in 1/N $1/N$ .

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0022924
• OSTI ID: 2461629
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 4 Vol. 17; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English