Topological Holography: The Example of The D2-D4 Brane System

Abstract

We propose a toy model for holographic duality. The model is constructed by embedding a stack of $N$ D2-branes and $K$ D4-branes (with one dimensional intersection) in a 6D topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2D BF theory (resp. 4D Chern-Simons theory) with ${\mathrm{GL}}_N$ (resp. ${\mathrm{GL}}_K$) gauge group. We propose that in the large $N$ limit the BF theory on ${\mathbb{R}}^2$ is dual to the closed string theory on ${\mathbb{R}}^2\times {\mathbb{R}}_{+}\times S^3$ with the Chern-Simons defect on $\mathbb{R}\times {\mathbb{R}}_{+}\times S^2$. As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection -- the algebra is the Yangian of ${\mathfrak{gl}}_K$. We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using a D3-D5 brane configuration in type IIB -- using supersymmetric twist and $\Omega$-deformation.

arXiv commentv4: Minor revision based on reviewer's report. Submission to SciPost

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• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Superspin chains from superstring theory
• Maximally twisted eleven-dimensional supergravity
• Twisted eleven-dimensional supergravity
• Twisted holography of defect fusions
• Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain
• Twisted holography on AdS${}_3\times S^3\times K3$ & the planar chiral algebra
• Embedding Integrable Superspin Chain in String Theory
• R-matrices and Miura operators in 5d Chern-Simons theory
• A domain wall in twisted M-theory
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• On a Gravity Dual to Flavored Topological Quantum Mechanics
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows