## Topological holography: The example of the D2-D4 brane system

Nafiz Ishtiaque, Seyed Faroogh Moosavian, Yehao Zhou

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

- doi: 10.21468/SciPostPhys.9.2.017
- Submissions/Reports

### Abstract

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.

### Cited by 7

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Nafiz Ishtiaque, -
^{1}^{2}Seyed Faroogh Moosavian, -
^{1}^{2}Yehao Zhou

- Gouvernement du Canada / Government of Canada
- Ministry of Research and Innovation (Canada, Ontario, Min Res&Innov) (through Organization: Ministry of Research, Innovation and Science - Ontario [MRIS])