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

TL;DR

This paper explores the geometric structures underlying the Hitchin topological sigma model, revealing that the target space geometry is Poisson--quasi--Nijenhuis, a generalization of generalized complex geometry, and discusses reduction procedures within this framework.

Contribution

It demonstrates that the BV master equations imply Poisson--quasi--Nijenhuis geometry and extends the understanding of symmetry reduction in the Hitchin model.

Findings

Target space geometry is Poisson--quasi--Nijenhuis, generalizing generalized complex geometry.

Gauging and reduction procedures are compatible with this geometric framework.

The resulting geometry from BV equations relates to but extends previous models by Lin and Tolman.

Abstract

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. We find that the geometry resulting form the BV master equation is closely related to but more general than that recently described by Lin and Tolman, suggesting a natural framework for the study of reduction of Poisson--quasi--Nijenhuis manifolds.