Mathematics – Differential Geometry
Scientific paper
2007-04-20
Commun.Math.Phys.281:469-497,2008
Mathematics
Differential Geometry
32 pages. This is the revised version which is going to appear in Commu. in Math. Physics. A few minor errors in version 2 are
Scientific paper
10.1007/s00220-008-0482-9
It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized K\"ahler manifolds is in perfect agreement with the physical notion of general $(2,2)$ gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on $H$-twisted generalized complex manifolds. If the manifold satisfies the $\bar{\partial}\partial$-lemma, we establish the equivariant formality theorem. If in addition, the manifold satisfies the generalized K\"ahler condition, we prove the Kirwan injectivity in this setting. We then consider the Hamiltonian action of a torus on an $H$-twisted generalized Calabi-Yau manifold and extend to this case the Duistermaat-Heckman theorem for the push-forward measure. As a side result, we show in this paper that the generalized K\"ahler quotient of a generalized K\"ahler vector space can never have a (cohomologically) non-trivial twisting. This gives a negative answer to a question asked by physicists whether one can construct $(2,2)$ gauged linear sigma models with non-trivial fluxes.
No associations
LandOfFree
The Equivariant cohomology theory of twisted generalized complex manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Equivariant cohomology theory of twisted generalized complex manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Equivariant cohomology theory of twisted generalized complex manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-230250