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Twisted holography on AdS$_3 \times S^3 \times K3 $ & the planar chiral algebra
by Víctor E. Fernández, Natalie M. Paquette, Brian R. Williams
Submission summary
| Authors (as registered SciPost users): | Natalie Paquette |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2404.14318v2 (pdf) |
| Date submitted: | 2024-09-25 04:10 |
| Submitted by: | Paquette, Natalie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this work, we revisit and elaborate on twisted holography for AdS$_3 \times S^3 \times X$ with $X= T^4$, 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 $N \rightarrow \infty$, 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 $1/N$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
We are grateful to the anonymous referee for their report and feedback on the draft.
In view of their comments, we have made the following changes:
1.) A more detailed discussion about the notion of twisting espoused in this paper, particularly twisting supergravity, on page 1.
2.) Added a footnote on page 2 with comments about the case of AdS3xS3XS3xS1.
3.) Corrected the typo pointed out in equation 2.5.11.
4.) Clarified that the appearance of C^{22} comes from H^2(K3), on the same page.