Branes and toric geometry
Naichung Conan Leung,Cumrun Vafa +1 more
Reads0
Chats0
TLDR
In this article, it was shown that toric geometry can be used to translate a brane configuration to geometry and that the skeletons of toric space are identified with the brane configurations.Abstract:
We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry involves hypersurfaces in toric varieties (such as P^2 blown up at more than 3 points) presents a challenge for the brane picture. We also find a simple physical explanation of Batyrev's construction of mirror pairs of Calabi-Yau manifolds using T-duality.read more
Citations
More filters
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.
Journal ArticleDOI
Brane Dimers and Quiver Gauge Theories
TL;DR: In this paper, a brane tiling is constructed for non-compact 3-dimensional toric Calabi-Yau manifolds, which can be represented as a periodic tiling of the plane.
Posted Content
Mirror symmetry, D-branes and counting holomorphic discs
Mina Aganagic,Cumrun Vafa +1 more
TL;DR: In this paper, the authors consider a class of special Lagrangian subspaces of Calabi-Yau manifolds and identify their mirrors, using the derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry.
Journal ArticleDOI
Gauge theories from toric geometry and brane tilings
TL;DR: In this paper, a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity is provided, combining information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings.
Journal ArticleDOI
Brane dimers and quiver gauge theories
TL;DR: In this paper, a brane tiling is constructed for non-compact 3-dimensional toric Calabi-Yau manifolds, which can be represented as a periodic tiling of the plane.
References
More filters
Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Book
Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces
TL;DR: In this article, the Duistermaat-Heckman theorem multiplicities as invariants of reduced spaces partition functions are defined and examples of Kaehler structures on toric varieties.