Topological strings on noncommutative manifolds

By A. Kapustin. 2003

156 citations recorded by the source corpus.

We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5559de3979ccd16c95f5f4b769c410af2db9fd3e

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In Geometry and Topology

1. M. Graña
2. E. Witten
3. A. Kapustin
4. G. Moore
5. L. Martucci
6. A. Tomasiello
7. D. Waldram
8. P. Aspinwall

In Nuclear and High Energy Physics

1. M. Graña
2. D. Lust
3. A. Tomasiello
4. E. Witten
5. G. Moore
6. D. Waldram
7. A. Kapustin
8. L. Martucci

In Statistical and Nonlinear Physics

1. M. Graña
2. E. Witten
3. D. Lust
4. D. Waldram
5. G. Moore
6. M. Gualtieri
7. A. Kapustin
8. A. Tomasiello

Citations in the corpus

• 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].”
• Lectures on the Langlands program and conformal field theory (2005, result): “ty in four-dimensional gauge theories and the Langlands correspondence that was mentioned in the Introduction. Examples of “non-commutative” D-branes related to D-modules have also been considered in [79], and in fact they are 52These dual Hitchin fibrations (restricted to the open subsets of stable ”
• Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes (2003, background): “The latter is important for several aspects of topological B-branes (see [22] for a recent discussion, in which also Clifford(d,d) spinors appear) and mirror symmetry [23].”
• Generalized structures of N=1 vacua (2005, methodology): “Let us now see all this more precisely, following [8, 9].”
• Deformation quantization of gerbes (2005, background): “or Fourier integral operators or by index theorems such as in [MMS]. Among the applications other than index theory, we would like to mention dualities between gerbes and noncommutative spaces, as in [Kapu], [Bl], [BBP], [MR1], [MR2]. The deformation-theoretical role of the first Rozansky-Witten clas”
• Generalized Complex Geometry (2004, background): “of quantization of Poisson structures, we are viewing them here as genuine (finite) deformations of the generalized complex structure. For more details about this distinction and its consequences, see [19],[16]. 6 Generalized complex branes In this section we introduce the natural “sub-objects” of ge”
• 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].”
• Branes on Poisson varieties (2007, unknown): “Equation (15) has been studied in [20], where it was shown that it corresponds to a noncommutative version of the (1, 1) condition via the Seiberg-Witten transform on tori.”
• M-theory, exceptional generalised geometry and superpotentials (2008, background): “This description has proved very useful in, among other things: characterising supersymmetric backgrounds, finding new examples with non-zero fluxes and writing supersymmetric low-energy effective theories [5]–[25]; describing topological string theories and generic N = (2, 2) σ-models [26]–[39]; as”
• T-duality and closed string non-commutative (doubled) geometry (2010, background): “So it would be interesting to see if non-commutative geometry arises for SU(3)×SU(3) group structure backgrounds in a natural way (see also [61]).”
• Generalized Complex Manifolds and Supersymmetry (2004, background): “Further, in topological models, the relevance of generalized complex structures has been demonstrated in [17] (see also [18]).”
• Topological sigma-models with H-flux and twisted generalized complex manifolds (2004, background): “[9], where the relation with GCstructures was first noted.”
• Dirichlet Branes and Mirror Symmetry (2009, methodology): “The concept of mirror symmetry evolved in the late 1980’s out of the study of superstring compactification, and received its first precise formulation in the 1991 work of Candelas, de la Ossa, Green, and Parkes [85] conjecturing (on the basis of solid physical arguments) a formula for the number of ”