Extending the Picard-Fuchs system of local mirror symmetry
Brian Forbes,Masao Jinzenji +1 more
TLDR
In this paper, an extended set of differential operators for local mirror symmetry was proposed, and a conjecture for intersection theory for such a set of operators was uncovered, along with operators on several examples of type X =KS through similar techniques.Abstract:
We propose an extended set of differential operators for local mirror symmetry. If X is Calabi-Yau such that dimH4(X,Z)=0, then we show that our operators fully describe mirror symmetry. In the process, a conjecture for intersection theory for such X is uncovered. We also find operators on several examples of type X=KS through similar techniques. In addition, open string Picard-Fuchs systems are considered.read more
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Direct integration for general Omega backgrounds
Min-xin Huang,Albrecht Klemm +1 more
TL;DR: In this paper, Huang et al. extended the direct integration method of the holomorphic anomaly equations to general non-compact Calabi-Yau three-folds and showed that the modularity and boundary conditions provided by the perturbative terms as well as by the gap condition at the conifold are sufficient to solve the generalized theory.
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Direct integration for general Omega backgrounds
Min-xin Huang,Albrecht Klemm +1 more
TL;DR: In this article, the authors extended the direct integration method of the holomorphic anomaly equations to general Omega backgrounds for pure SU(2) N=2 Super-Yang-Mills theory and topological string theory on non-compact Calabi-Yau threefolds.
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Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
TL;DR: In this article, the quantum deformed version of rigid special geometry, which has its origin in the quantum mechanical behaviour of branes in the topological string B-model, is studied.
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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.
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Exact Kähler potential for Calabi-Yau fourfolds
Yoshinori Honma,Masahide Manabe +1 more
TL;DR: In this paper, the authors studied the quantum Kahler moduli space of Calabi-Yau fourfold manifold and derived the explicit form of the quantum-corrected Kahler potential.
References
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Phases of N = 2 theories in two dimensions
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
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
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On the Gauge Theory/Geometry Correspondence
Rajesh Gopakumar,Cumrun Vafa +1 more
TL;DR: The 't Hooft expansion of SU(N) Chern-Simons theory was shown to be exactly dual to topological closed string theory on the blow up of the conifold geometry in this paper.
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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.
Journal ArticleDOI
Geometric engineering of quantum field theories
TL;DR: In this paper, a local geometric realization of quantum field theories together with a local application of mirror symmetry is proposed to reduce non-trivial quantum field theory results to much better understood T -dualities of type 11 strings.