Recently, Costello proposed how to systematically apply Omega deformation on string theory and M-theory. Upon the deformation, one can discuss the exact topological holography of both M2 and M5 branes.

The goal of the talk is to review Costello’s formalism and to discuss a combined system of the M2 and M5 branes, which is the joint work with D. Gaiotto. The M2 brane worldvolume theory is 3d N=4 ADHM gauge theory, which is a self-mirror. The relevant degree of freedom associated to the M5 brane is $W_{1+\infty}$ Vertex Operator Algebra. I will explain how two systems interact each other and point out the connection to Y-algebra configuration, introduced by Gaiotto and Rapcak.