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Topological Holography: The Example of The D2D4 Brane System
by Nafiz Ishtiaque, Seyed Faroogh Moosavian, Yehao Zhou
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Nafiz Ishtiaque · Seyed Faroogh Moosavian 
Submission information  

Preprint Link:  https://arxiv.org/abs/1809.00372v4 (pdf) 
Date accepted:  20200714 
Date submitted:  20200702 02:00 
Submitted by:  Ishtiaque, Nafiz 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
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.
Author comments upon resubmission
List of changes
1. Corrected several spellings, and a typo in eq. 5.
2. At the end of section 1 pointed out relevant new references that came out in the last couple of years.
3. Slightly expanded the introduction to appendix B to better clarify the motivation and logic behind the mathematical results to follow.
4. Some footnotes have been moved to the main text.
5. Commented on the special nature of the lack of backreaction in the 4d ChernSimons theory after eq. 14 with references to literature with different examples with and without backreaction.
Published as SciPost Phys. 9, 017 (2020)