Geometric Langlands Twists of N = 4 Gauge Theory from Derived Algebraic Geometry

Understand

We develop techniques for describing the derived moduli spaces of solutions to the equations of motion in twists of supersymmetric gauge theories as derived algebraic stacks.

• We introduce a holomorphic twist of N=4 supersymmetric gauge theory and compute the derived moduli space.
• We then compute the moduli spaces for the Kapustin-Witten topological twists as its further twists.
• The resulting spaces for the A- and B-twist are closely related to the de Rham stack of the moduli space of algebraic bundles and the de Rham moduli space of flat bundles, respectively.