Remarks on quiver gauge theories from open topological string theory

Carqueville, Nils; Velez, Alexander Quintero

doi:10.1007/jhep03(2010)129

Cited by 5 publications

(7 citation statements)

References 69 publications

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“…is also a tilting collection for D(Coh B 4 ), the B-brane category on B 4 [56]. 9 The fractional branes we are looking for are related to the line bundles (2.40), but they are somewhat more complicated objects in D(Coh B 4 ).…”

Section: D Toric Fano Varieties and Brane Charge Dictionariesmentioning

confidence: 99%

Toric Fano varieties and Chern-Simons quivers

Closset

Cremonesi

2012

J. High Energ. Phys.

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In favourable cases the low energy dynamics of a stack of M2-branes at a toric Calabi-Yau fourfold singularity can be described by an N=2 supersymmetric Chern-Simons quiver theory, but there still does not exists an "inverse algorithm" going from the toric data of the CY_4 to the CS quiver. We make progress in that direction by deriving CS quiver theories for M2-branes probing cones over a large class of geometries Ypq(B_4), which are S^3/Z_p bundles over toric Fano varieties B_4. We rely on the type IIA understanding of CS quivers, giving a firm string theory footing to our CS theories. In particular we give a derivation of some previously conjectured CS quivers in the case B_4= CP^1*CP^1, as field theories dual to M-theory backgrounds with nontrivial torsion G_4 fluxes.Comment: 92 pages and many figures. v2: section 7.3 on quivers with equal ranks expanded. v3: added a referenc

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Section: D Toric Fano Varieties and Brane Charge Dictionariesmentioning

confidence: 99%

Toric Fano varieties and Chern-Simons quivers

Closset

Cremonesi

2012

J. High Energ. Phys.

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“…The A ∞ -structure encodes the superpotential. There has been some progress towards equating the superpotential arising from the quiver relations and the superpotential arising from this A ∞ algebra [44], but to date a complete proof seems elusive.…”

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confidence: 99%

Quivers from Matrix Factorizations

Aspinwall

Morrison

2012

Commun. Math. Phys.

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We discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity. This method also yields explicit geometrical interpretations of D-branes (i.e., quiver representations) on a resolution given in terms of Grassmannians. As an example we analyze some non-toric singularities which are resolved by a single P 1 but have "length" greater than one. These examples have a much richer structure than conifolds. A picture is proposed that relates matrix factorizations in Landau-Ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions.

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“…The correlation functions are known to be constrained by BRST symmetry leading to interesting algebraic structures including in particular the A ∞ structure obeyed by correlators without bulk insertions [17,18], see [19,20,21,22,23,24] for recent papers exploiting algebraic structures to calculate superpotentials.…”

Section: )mentioning

confidence: 99%

D-brane superpotentials: Geometric and worldsheet approaches

2011

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From the worldsheet perspective, the superpotential on a D-brane wrapping internal cycles of a Calabi-Yau manifold is given as a generating functional for disk correlation functions. On the other hand, from the geometric point of view, D-brane superpotentials are captured by certain chain integrals. In this work, we explicitly show for branes wrapping internal 2-cycles how these two different approaches are related. More specifically, from the worldsheet point of view, D-branes at the Landau-Ginzburg point have a convenient description in terms of matrix factorizations. We use a formula derived by Kapustin and Li to explicitly evaluate disk correlators for families of D2-branes. On the geometry side, we then construct a three-chain whose period gives rise to the effective superpotential and show that the two expressions coincide. Finally, as an explicit example, we choose a particular compact Calabi-Yau hypersurface and compute the effective D2-brane superpotential in different branches of the open moduli space, in both geometric and worldsheet approaches. dx 2 dx 4 dx 5 .(3.23)Since J 0 and J 2 are independent of β, we can repeat the steps above and bring the correlator into the form of (3.21).In the next section, we will show that (3.21) coincides with the simplified expression for the chain integral that gives rise to the effective D-brane superpotential. In this manner, we establish an explicit map between the bulk-boundary correlation function computed by the matrix factorization technique and the superpotential chain integral in the geometric picture. Superpotentials from Chain IntegralsAs explained in section 2, D2-branes wrap holomorphic two-cycles of the internal Calabi-Yau space.These holomorphic cycles only exist at specific points in the closed-string moduli space, and hence

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Remarks on quiver gauge theories from open topological string theory

Cited by 5 publications

References 69 publications

Toric Fano varieties and Chern-Simons quivers

Toric Fano varieties and Chern-Simons quivers

Quivers from Matrix Factorizations

D-brane superpotentials: Geometric and worldsheet approaches

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