2006/10/25 by Anton Kapustin, Alessandro Tomasiello
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Field (mathematics) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Killing vector field #Manifold (fluid mechanics) #Moment (physics) #Quotient #Sigma #Sigma model #Vector field #hep-th
paper · pdf · doi:10.1088/1126-6708/2007/11/053
published as JHEP0711:053,2007 · 24 pages. v2: typos fixed, other minor corrections
arxiv created 2006/10/25 · openalex publication_date 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We find the conditions under which a Riemannian manifold equipped with a closed three-form and a vector field define an on--shell N=(2,2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized Kaehler structure, that the vector field preserves this structure, and that a so--called generalized moment map exists for it. By a theorem in generalized complex geometry, these conditions imply that the quotient is again a twisted generalized Kaehler manifold; this is in perfect agreement with expectations from the renormalization group flow. This method can produce new N=(2,2) models with NS flux, extending the usual Kaehler quotient construction based on Kaehler gauged sigma models.