The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction

Understand

We revisit our earlier work on the AKSZ formulation of topological sigma model on generalized complex manifolds, or Hitchin model.

• We show that the target space geometry geometry implied by the BV master equations is Poisson--quasi--Nijenhuis geometry recently introduced and studied by Sti\'enon and Xu (in the untwisted case).
• Poisson--quasi--Nijenhuis geometry is more general than generalized complex geometry and comprises it as a particular case.
• Next, we show how gauging and reduction can be implemented in the Hitchin model.