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The Equivariant Cohomology Theory of Twisted Generalized Complex Manifolds
Communications in Mathematical Physics (2008)
  • Yi Lin, Georgia Southern University
Abstract
It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler 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 ¯¯¯
-lemma, we establish the equivariant formality theorem. If in addition, the manifold satisfies the generalized Kähler 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 Kähler quotient of a generalized Kähler 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.
Keywords
  • Differential Geometry (math.DG),
  • High Energy Physics - Theory (hep-th),
  • Symplectic Geometry (math.SG)
Disciplines
Publication Date
July, 2008
DOI
10.1007/s00220-008-0482-9
Citation Information
Yi Lin. "The Equivariant Cohomology Theory of Twisted Generalized Complex Manifolds" Communications in Mathematical Physics Vol. 281 Iss. 2 (2008) p. 469 - 497 ISSN: 1432-0916
Available at: http://works.bepress.com/yi_lin/2/