SciPost Phys. 11, 077 (2021) ·
published 14 October 2021
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We study a four-dimensional domain wall in twisted M-theory. 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 M-theory 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 $U(1)$ Chern-Simons
theory, we reproduce the non-perturbative 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 M-theory, which is a
natural set-up for Twisted holography. Feynman diagram 1-loop computations in
the twisted-holographic 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 $N$ 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.
