Orbifold quasimap theory

Cheong, Daewoong; Ciocan-Fontanine, Ionuţ; Kim, Bumsig

doi:10.1007/s00208-015-1186-z

Cited by 60 publications

(113 citation statements)

References 29 publications

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“…It would be interesting to see if our results for vortex defects without dynamical vector multiplets can be used to compute the orbifold Gromov-Witten invariants, which have been studied only relatively recently [44]. Such a connection can be motivated by the fact that the mathematical formulas for the invariants proposed in [45] involve the ceiling and the floor functions (also known as the round-up and the round-down). It would be nice to develop field theoretical techniques for computing the Gromov-Witten invariants for both toric and non-toric orbifolds, which may lead to physical understanding of the so-called crepant resolution conjecture [46].…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric vortex defects in two dimensions

Hosomichi

Lee

Okuda

2018

J. High Energ. Phys.

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We study codimension-two BPS defects in 2d N = (2, 2) supersymmetric gauge theories, focusing especially on those characterized by vortex-like singularities in the dynamical or non-dynamical gauge field. We classify possible SUSY-preserving boundary conditions on charged matter fields around the vortex defects, and derive a formula for defect correlators on the squashed sphere. We also prove an equivalence relation between vortex defects and 0d-2d coupled systems. Our defect correlators are shown to be consistent with the mirror symmetry duality between Abelian gauged linear sigma models and Landau-Ginzburg models, as well as that between the minimal model and its orbifold. We also study the vortex defects inserted at conical singularities.

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Section: Discussionmentioning

confidence: 99%

Supersymmetric vortex defects in two dimensions

Hosomichi

Lee

Okuda

2018

J. High Energ. Phys.

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“…Remark 2.2. We make the above assumption so that the equivariant mirror theorem in [6,7] has an explicit mirror map.…”

Section: Line Bundles and Divisors Onmentioning

confidence: 99%

Central charges of T-dual branes for toric varieties

Fang

2020

Trans. Amer. Math. Soc.

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Given any equivariant coherent sheaf L on a compact semi-positive toric orbifold X , its SYZ T-dual mirror dual is a Lagrangian brane in the Landau-Ginzburg mirror. We prove the oscillatory integral of the equivariant superpotential in the Landau Ginzburg mirror over this Lagrangian brane is the genus-zero 1-descendant Gromov-Witten potential with a Gamma-type class of L inserted. DFS((CHere FS is a kind of Fukaya-Seidel category, and Coh is the category of coherent sheaves. This statement is proved using different setups of Fukaya-Seidel categories [1,10].There are more structures in these categories of branes. There should be a BPS central charge or simply central charge associated to each brane, either in A or B-model. These central charges play important roles in the stability conditions of Bridgeland [4].The canonical central charge of a Lagrangian submanifold Ξ in a Calabi-Yau manifold (an A-brane) is the integration of the Calabi-Yau form Ξ Ω.

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“…Then Theorem 3.3 can also be stated in terms of the S-extended I-function for root stacks without change. We also refer to [15] and [12] for the S-extended I-function for toric stacks. As mentioned in [26], [15], [30], the non-extended Ifunction only determines the restriction of the J-function to the small parameter space H 2 (X D,r , C) ⊂ H 2 CR (X D,r , C).…”

Section: 4mentioning

confidence: 99%