Topological Holography: The Example of The D2-D4 Brane System
| Autor: | Ishtiaque, Nafiz, Moosavian, Seyed Faroogh, Zhou, Yehao |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | SciPost Phys. 9, 017 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.21468/SciPostPhys.9.2.017 |
| Popis: | 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. Comment: v4: Minor revision based on reviewer's report. Submission to SciPost |
| Databáze: | arXiv |
| Externí odkaz: |
|