SciPost Phys. 11, 077 (2021) ·
published 14 October 2021

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We study a fourdimensional domain wall in twisted Mtheory. The domain wall
is engineered by intersecting D6 branes in the type IIA frame. We identify the
classical algebra of operators on the domain wall in terms of a higher vertex
operator algebra, which describes the holomorphic subsector of a 4d
$\mathcal{N}=1$ supersymmetric field theory, and compute the associated mode
algebra. We conjecture that the quantum deformation of the classical algebra is
isomorphic to the bulk algebra of operators from which we establish twisted
holography of the domain wall.
SciPost Phys. 10, 105 (2021) ·
published 14 May 2021

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In the twisted Mtheory setting, various types of fusion of M2 and M5 branes
induce coproducts between the algebra of operators on M2 branes and the algebra
of operators on M5 branes. By doing a perturbative computation in the gravity
side, which is captured by the 5d topological holomorphic $U(1)$ ChernSimons
theory, we reproduce the nonperturbative coproducts.
SciPost Phys. 10, 029 (2021) ·
published 5 February 2021

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We derive the simplest commutation relations of operator algebras associated
to M2 branes and an M5 brane in the $\Omega$deformed Mtheory, which is a
natural setup for Twisted holography. Feynman diagram 1loop computations in
the twistedholographic dual side reproduce the same algebraic relations.
SciPost Phys. 9, 017 (2020) ·
published 5 August 2020

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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.