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Orbifold Gromov-Witten Invariants and Topological Strings
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In this paper, a pedagogical approach to the computation of Gromov-Witten invariants using mirror symmetry and topological string theory is proposed, focusing on the orbifold C 3 /Z3.Abstract:
In this contribution I propose a (hopefully) pedagogical ap- proach to the computation of orbifold Gromov-Witten invariants using mirror symmetry and topological string theory, focusing on the orbifold C 3 /Z3. Recent B-model developments on the mirror side, which led to predictions for "open orbifold Gromov-Witten invariants" of C 3 /Z3, are also addressed. This contribution is based on the results of (1) and (9).read more
Citations
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Exact Results for Topological Strings on Resolved Y p,q Singularities
TL;DR: In this paper, the authors obtained exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories.
Journal ArticleDOI
Exact results for topological strings on resolved Y(p,q) singularities
TL;DR: In this paper, the authors obtained exact results for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories.
Journal ArticleDOI
Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry
Andrea Brini,Renzo Cavalieri +1 more
TL;DR: In this article, the authors develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry.
Journal ArticleDOI
Crepant Resolutions of $\mathbb{C}^3/\mathbb{Z}_4$ and the Generalized Kronheimer Construction (in view of the Gauge/Gravity Correspondence)
Ugo Bruzzo,Annamaria Fino,Pietro Fré,Pietro Antonio Grassi,Pietro Antonio Grassi,Dimitri Markushevich +5 more
TL;DR: In this article, the authors studied the Kahler quotient resolution of the orbifold ℂ 3 ∕ Z 4, comparing with the results of a toric description of the same.
Posted Content
A formula for the total permutation-equivariant K-theoretic Gromov-Witten potential
TL;DR: In this article, the authors give a summation over graphs type formula for the permutation-equivariant K-theoretic Gromov-Witten total potential of a projective manifold X in terms of cohomological GW invariants of X. They achieve this by describing combinatorially the Kawasaki strata of the moduli spaces of stable maps to X.
References
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A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.
Journal ArticleDOI
Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
TL;DR: In this paper, the authors developed techniques to compute higher loop string amplitudes for twisted N = 2 theories with ε = 3 (i.e. the critical case) by exploiting the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured by a master anomaly equation.
Book
Mirror Symmetry
Eric Zaslow,Ravi Vakil,Kentaro Hori,Richard P. Thomas,Cumrun Vafa,Albrecht Klemm,Rahul Pandharipande,Sheldon Katz +7 more
TL;DR: In this paper, the authors proved mirror symmetry for supersymmetric sigma models on Calabi-Yau manifolds in 1+1 dimensions and showed that the equivalence of the gauged linear sigma model embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices.
Book
Mirror symmetry and algebraic geometry
David A. Cox,Sheldon Katz +1 more
TL;DR: The quintic threefold Toric geometry Mirror symmetry constructions Hodge theory and Yukawa couplings Moduli spaces Gromov-Witten invariants Quantum cohomology Localization Quantum differential equations The mirror theorem Conclusion Singular varieties Physical theories Bibliography Index as mentioned in this paper
Journal ArticleDOI
The Topological Vertex
TL;DR: In this paper, a cubic field theory was constructed for all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefold.