Abstract
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.
Highlights
Scalars make up the remainder of gC
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
We find that it is consistent with supersymmetry to set this quantized flux parameter to zero
Summary
We construct a Euclidean continuation of the six-dimensional (2, 0) theory on a three-dimensional spherical background. We consider a squashed three-sphere which preserves the round form of the metrics on the base and the fiber, but takes their ratio of radii to be l/2, where l ∈ R+ is a parameter of the construction. Preserving supersymmetry on a squashed three sphere will require us to activate various background supergravity fields, and we describe the precise form of these. We wish to study a configuration which is compatible with replacing R3 with a general threemanifold M3 while preserving supersymmetry It follows that our choice of background supergravity fields must be compatible with topological twisting.
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