Topological A-Type Models with Flux

Abstract

We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that the fluxes are related to deformations of the Courant bracket which generalize the twist by a closed 3-from $H$, in the sense that satisfying the AKSZ master equation implies the integrability conditions for an almost generalized complex structure with respect to the deformed Courant bracket. In addition, the master equation imposes conditions on the fluxes that generalize $dH=0$. The membrane model can be defined on a large class of $U(m)$- and $U(m)\times U(m)$-structure manifolds, including geometries inspired by $(1,1)$ supersymmetric $\sigma$-models with additional supersymmetries due to almost complex (but not necessarily complex) structures in the target space. Furthermore, we show that the model can be defined on three particular half-flat manifolds related to the Iwasawa manifold. When only $H$-flux is turned on it is possible to obtain a topological string model, which we do for the case of a Calabi-Yau with a closed 3-form turned on. The simplest deformation from the A-model is due to the $(2,0)+(0,2)$ component of a non-trivial $b$-field. The model is generically no longer evaluated on holomorphic maps and defines new topological invariants. Deformations due to $H$-flux can be more radical, completely preventing auxiliary fields from being integrated out.

30 pages. v2: Improved Version. References added. v3: Minor changes, published in JHEP

References in corpus (19)

• Doubled Geometry and T-Folds
• Generalised T-Duality and Non-Geometric Backgrounds
• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Generalized Kahler manifolds and off-shell supersymmetry
• T-duality with H-flux: non-commutativity, T-folds and G x G structure
• Generalized Kahler Geometry from supersymmetric sigma models
• T-duality and Generalized Kahler Geometry
• The biHermitian topological sigma model
• Linearizing Generalized Kahler Geometry
• Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• The Ricci Curvature of Half-flat Manifolds
• On the symmetries of special holonomy sigma models
• The general (2,2) gauged sigma model with three--form flux
• Computing Amplitudes in topological M-theory
• Topological twisted sigma model with H-flux revisited
• An Alternative Topological Field Theory of Generalized Complex Geometry

Cited by in corpus (4)

• Double field theory for the A/B-models and topological S-duality in generalized geometry
• AKSZ constructions for topological membranes on $G_2$-manifolds
• Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives
• Two-Dimensional Supersymmetric Sigma Models on Almost-Product Manifolds and Non-Geometry