SciPost Phys. 9, 017 (2020) ·
published 5 August 2020

· pdf
We propose a toy model for holographic duality. The model is constructed by
embedding a stack of $N$ D2branes and $K$ D4branes (with one dimensional
intersection) in a 6D topological string theory. The worldvolume theory on the
D2branes (resp. D4branes) is 2D BF theory (resp. 4D ChernSimons 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 ChernSimons
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 D2D4 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
ChernSimons 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 D3D5 brane configuration in type IIB  using supersymmetric
twist and $\Omega$deformation.