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

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 Stiénon 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.

38 pages, no figures, LaTex. One paragraph in sect. 6 and 3 references added

References in corpus (10)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Generalized Kahler manifolds and off-shell supersymmetry
• Lectures on Generalized Complex Geometry and Supersymmetry
• Hamiltonian symmetries and reduction in generalized geometry
• The biHermitian topological sigma model
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Generalized complex geometry and supersymmetric non-linear sigma models
• Generalized geometry, equivariant $\bar{\partial }\partial$-lemma, and torus actions
• BiHermitian Supersymmetric Quantum Mechanics
• Reduction and submanifolds of generalized complex manifolds

Cited by in corpus (9)

• Lectures on AKSZ Sigma Models for Physicists
• Poisson quasi-Nijenhuis structures with background
• Gauging the Poisson sigma model
• The Lie algebroid Poisson sigma model
• The gauging of BV algebras
• Topological A-Type Models with Flux
• AKSZ construction from reduction data
• Supersymmetric Poisson and Poisson-supersymmetric sigma models
• 2D and 3D topological field theories for generalized complex geometry