Complex Chern-Simons from M5-branes on the Squashed Three-Sphere

Understand

We derive an equivalence between the (2,0) superconformal M5-brane field theory dimensionally reduced on a squashed three-sphere, and Chern-Simons theory with complex gauge group.

• In the reduction, the massless fermions obtain an action which is second order in derivatives and are reinterpreted as ghosts for gauge fixing the emergent non-compact gauge symmetry.
• A squashing parameter in the geometry controls the imaginary part of the complex Chern-Simons level.