| Summary: | 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.
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