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88
SU (3) × SU (3) compactification and mirror duals of magnetic fluxes
, 2009
"... This paper analyses type II string theories in backgrounds which admit an SU(3)×SU(3) structure. Such backgrounds are designed to linearly realize eight out of the original 32 supercharges and as a consequence the lowenergy effective action can be written in terms of couplings which are closely rel ..."
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Cited by 65 (3 self)
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This paper analyses type II string theories in backgrounds which admit an SU(3)×SU(3) structure. Such backgrounds are designed to linearly realize eight out of the original 32 supercharges and as a consequence the lowenergy effective action can be written in terms of couplings which are closely related to the couplings of fourdimensional N = 2 theories. This generalizes the previously studied case of SU(3) backgrounds in that the left and rightmoving sector each have a different globally defined spinor. Given a truncation to a finite number of modes, these backgrounds lead to a conventional fourdimensional lowenergy effective theory. The results are manifestly mirror symmetric and give terms corresponding to the mirror dual couplings of CalabiYau compactifications with magnetic fluxes. It is argued, however, that generically such backgrounds are nongeometric and hence the supergravity analysis is not strictly valid. Remarkably, the naive generalization of the geometrical expressions nonetheless appears to give the correct lowenergy effective theory.
A sigma model field theoretic realization of Hitchin’s generalized complex geometry
, 2004
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Topological strings in generalized complex space
, 2006
"... A twodimensional topological sigmamodel on a generalized CalabiYau target space X is defined. The model is constructed in BatalinVilkovisky formalism using only a generalized complex structure J and a pure spinor ρ on X. In the present construction the algebra of Qtransformations automatically ..."
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Cited by 37 (1 self)
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A twodimensional topological sigmamodel on a generalized CalabiYau target space X is defined. The model is constructed in BatalinVilkovisky formalism using only a generalized complex structure J and a pure spinor ρ on X. In the present construction the algebra of Qtransformations automatically closes offshell, the model transparently depends only on J, the algebra of observables and correlation functions for topologically trivial maps in genus zero are easily defined. The extended moduli space appears naturally. The familiar action of the twisted N = 2 CFT can be recovered after a gauge fixing. In the open case, we consider an example of generalized deformation of complex structure by a holomorphic Poisson bivector β and recover holomorphic noncommutative Kontsevich ∗product.
Hamiltonian perspective on generalized complex structure
, 2005
"... In this note we clarify the relation between extended worldsheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant b ..."
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Cited by 31 (2 self)
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In this note we clarify the relation between extended worldsheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant bracket and the group of local canonical transformations of the cotangent bundle of the loop space. Indeed this fact explains the natural relation between the worldsheet and the geometry of T ⊕ T ∗. We discuss Dbranes in this perspective.
The Hitchin functionals and the topological Bmodel at one loop
"... Please refer to [1] for the complete list of references and the details. ..."
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Cited by 31 (2 self)
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Please refer to [1] for the complete list of references and the details.
Towards Minkowski vacua in type II string compactifications
, 2007
"... We study the vacuum structure of compactifications of type II string theories on orientifolds with SU(3) × SU(3) structure. We argue that generalised geometry enables us to treat these nongeometric compactifications using a supergravity analysis in a way very similar to geometric compactifications ..."
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Cited by 29 (2 self)
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We study the vacuum structure of compactifications of type II string theories on orientifolds with SU(3) × SU(3) structure. We argue that generalised geometry enables us to treat these nongeometric compactifications using a supergravity analysis in a way very similar to geometric compactifications. We find supersymmetric Minkowski vacua with all the moduli stabilised at weak string coupling and all the tadpole conditions satisfied. Generically the value of the moduli fields in the vacuum is parametrically controlled and can be taken to arbitrarily large values.
Generalized complex geometry, generalized branes and the Hitchin sigma model
 JHEP 0503 (2005) 022 [arXiv:hepth/0501062
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Spaces of stability conditions
"... Abstract. Stability conditions are a mathematical way to understand Πstability for Dbranes in string theory. Spaces of stability conditions seem to be related to moduli spaces of conformal field theories. This is a survey article describing what is currently known about spaces of stability conditi ..."
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Cited by 27 (3 self)
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Abstract. Stability conditions are a mathematical way to understand Πstability for Dbranes in string theory. Spaces of stability conditions seem to be related to moduli spaces of conformal field theories. This is a survey article describing what is currently known about spaces of stability conditions, and giving some pointers for future research. 1.
Lectures on Generalized Complex Geometry and Supersymmetry
, 2006
"... These are the lecture notes from the 26th Winter School ”Geometry and Physics”, Czech Republic, Srni, January 14 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry ..."
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Cited by 25 (4 self)
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These are the lecture notes from the 26th Winter School ”Geometry and Physics”, Czech Republic, Srni, January 14 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to twodimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kähler and generalized CalabiYau manifolds and explain their appearance in physics.
Hamiltonian symmetries and reduction in generalized geometry
"... Abstract. Given a close 3form H ∈ Ω3 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω2 0 (M). We define the group of Htwisted Hamiltonian symmetries Ham(M, J; H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which lea ..."
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Cited by 23 (5 self)
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Abstract. Given a close 3form H ∈ Ω3 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω2 0 (M). We define the group of Htwisted Hamiltonian symmetries Ham(M, J; H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which leads to generalized complex reduction much the same way as symplectic reduction is constructed. The definitions and constructions are natural extensions of the corresponding ones in symplectic geometry. We describe cutting in generalized complex geometry to show that a general phenomenon in generalized geometry is that topology change is often accompanied by twisting (class) change. 1.