Twisted Supergravity and Koszul Duality: A case study in AdS${}_3$

Abstract

In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS${}_3\times S^3\times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory $Sy{m}^N(T^4)$ as $N\to \infty$. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the $N\to \infty$ limit of the twisted gravitational theory. We emphasize the role of $\text{Koszul duality}$---a ubiquitous mathematical notion to which we provide a friendly introduction---in field theory and string theory. After illustrating the appearance of Koszul duality in the "toy" example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper.

80 pages, 9 figures

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• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• Feynman diagrams and $\Omega$-deformed M-theory
• Superspin chains from superstring theory
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Maximally twisted eleven-dimensional supergravity
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Twisted eleven-dimensional supergravity
• Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories
• Superstrings in Thermal Anti-de Sitter Space
• Twisted holography of defect fusions
• Twisted String Theory in Anti-de Sitter Space
• Localization on $Ad{S}_3\times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity
• Twisted holography on AdS${}_3\times S^3\times K3$ & the planar chiral algebra
• R-matrices and Miura operators in 5d Chern-Simons theory
• A domain wall in twisted M-theory
• One-loop corrections to the celestial chiral algebra from Koszul Duality
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Structure of the $\mathcal{N}=4$ chiral algebra
• Twisting BFSS & IKKT