Topological sigma-models with H-flux and twisted generalized complex manifolds
By A. Kapustin, Yi Li. 2004
161 citations recorded by the source corpus.
We study the topological sector of N = 2 sigma-models with HH-flux. It has been known for a long time that the target-space geometry of these theories is not Kahler and can be described in terms of a pair of complex structures, which do not commute, in general, and are parallel with respect to two different connections with torsion. Recently an alternative description of this geometry was found, which involves a pair of commuting twisted generalized complex structures on the target space. In this paper, we define and study the analogs of A and B-models for N = 2 sigma-models with HH-flux and show that the results are naturally expressed in the language of twisted generalized complex geometry. For example, the space of topological observables is given by the cohomology of a Lie algebroid associated to one of the two twisted generalized complex structures. We determine the topological scalar product, which endows the algebra of observables with the structure of a Frobenius algebra. We also discuss mirror symmetry for twisted generalized Calabi-Yau manifolds.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1fc00abc2a2a9ff1cfaa8ebee2320f03e91e6bc0
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Citations in the corpus
- Generalized Kähler Geometry (2010, background): “This equivalence, obtained in the author’s thesis [23], was followed by a number of results, such as those contained in [8,10,17,19,22,24,29,30,32,35], which are not easily accessed purely from the bi-Hermitian point of view.”
- Hitchin functionals in N = 2 supergravity (2005, background): “Similarly it has been possible [29, 32] to generalize the notion of topological strings away from backgrounds with SU (3)-structure (such as Calabi–Yau manifolds) to more general spaces with SU (3) × SU (3) structure, again using the spinors Φ±.”
- D-branes on general Script N = 1 backgrounds: superpotentials and D-terms (2006, background): “The superpotentials we find may be adopted for the topological branes [11–15] of the associated topological models [5, 11, 16].”
- Generalized N=1 orientifold compactifications and the Hitchin functionals (2006, background): “Evidence for this identification is provided by comparing the generalized type IIA and type IIB superpotentials.”
- Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, background): “[ 30 ]). The notion of infinitesimal Hamiltonian symmetry in (untwisted) generalized geometry is given by [22], in remark 5.2 and proposition 5.3.”
- Generalized structures of N=1 vacua (2005, methodology): “Let us now see all this more precisely, following [8, 9].”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, background): “They are known as generalized topological sigma-models, since their correlators depend on a generalized complex structure on the target M [22, 23].”