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

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 GLN (resp. GLK) gauge group. We propose that in the large N limit the BF theory on R2 is dual to the closed string theory on R2 × R+ × S3 with the Chern-Simons defect on R × R+ × S2. 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 glK. 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 Ω-deformation.