Generalized Complex Manifolds and Supersymmetry

Lindström, Ulf; Minasian, Ruben; Tomasiello, Alessandro; Zabzine, Maxim

doi:10.1007/s00220-004-1265-6

Cited by 119 publications

(182 citation statements)

References 28 publications

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“…[12][13][14][15][16][17][18][19][20][21][22][23][24][25]. All these were somehow unsatisfactory either because they remained confined to the analysis of geometrical aspects of the sigma models or because they yielded field theories, which though interesting in their own, were not directly suitable for quantization, showed no apparent kinship with Witten's A and B models and were of limited relevance for string theory.…”

Section: Introductionmentioning

confidence: 99%

The biHermitian topological sigma model

Zucchini¹

2006

J. High Energy Phys.

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BiHermitian geometry, discovered long ago by Gates, Hull and Roček, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. By using the twisting procedure proposed by Kapustin and Li, we work out the type A and B topological sigma models for a general biHermtian target space, we write down the explicit expression of the sigma model's action and BRST transformations and present a computation of the topological gauge fermion and the topological action.

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Section: Introductionmentioning

confidence: 99%

The biHermitian topological sigma model

Zucchini¹

2006

J. High Energy Phys.

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“…The calculation of the second bracket is lengthy but straightforward. The coordinate expressions coincide with those given in [12]. Therefore we give only the final result of the calculation.…”

Section: Supersymmetry In Phase Spacementioning

confidence: 52%

“…The first order actions discussed in [11] and [12] can be thought of as phase space actions and therefore the Hamiltonian formalism should naturally arise in the problem. Indeed the Hamiltonian formalism offers a deep insight on the relation between the world-sheet and the geometry of T ⊕ T * .…”

Section: Discussionmentioning

confidence: 99%

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Hamiltonian Perspective on Generalized Complex Structure

Zabzine

2006

Commun. Math. Phys.

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In this note we clarify the relation between extended world-sheet 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 world-sheet and the geometry of T ⊕ T * . We discuss D-branes in this perspective.

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“…Most of the work done until now in this framework was on generalized, complex and Kähler structures [8] and this work was motivated by applications to supersymmetry in string theory [13]. Other generalized structures that were considered are the almost product structures [17,20], the almost tangent structures [17] and the almost contact structures [11,18].…”

Section: Introductionmentioning

confidence: 99%

Generalized CRF-structures

Vaisman

2008

Geom Dedicata

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ABSTRACT. A generalized F-structure is a complex, isotropic subbundle E of T c M ⊕ T * c M (T c M = T M ⊗ R C and the metric is defined by pairing) such that E ∩Ē ⊥ = 0. If E is also closed by the Courant bracket, E is a generalized CRF-structure. We show that a generalized F-structure is equivalent with a skew-symmetric endomorphism Φ of T M ⊕ T * M that satisfies the condition Φ 3 + Φ = 0 and we express the CRF-condition by means of the CourantNijenhuis torsion of Φ. The structures that we consider are generalizations of the F-structures defined by Yano and of the CR (Cauchy-Riemann) structures. We construct generalized CRF-structures from: a classical F-structure, a pair (V, σ) where V is an integrable subbundle of T M and σ is a 2-form on M , a generalized, normal, almost contact structure of codimension h. We show that a generalized complex structure on a manifoldM induces generalized CRFstructures into some submanifolds M ⊆M . Finally, we consider compatible, generalized, Riemannian metrics and we define generalized CRFK-structures that extend the generalized Kähler structures and are equivalent with quadruples (γ, F + , F − , ψ), where (γ, F ± ) are classical, metric CRF-structures, ψ is a 2-form and some conditions expressible in terms of the exterior differential dψ and the γ-Levi-Civita covariant derivative ∇F ± hold. If dψ = 0, the conditions reduce to the existence of two partially Kähler reductions of the metric γ. The paper ends by an Appendix where we define and characterize generalized Sasakian structures.* 2000 Mathematics Subject Classification: 53C15 .

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Generalized Complex Manifolds and Supersymmetry

Cited by 119 publications

References 28 publications

The biHermitian topological sigma model

The biHermitian topological sigma model

Hamiltonian Perspective on Generalized Complex Structure

Generalized CRF-structures

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