Toric duality, Seiberg duality and Picard‐Lefschetz transformations

@article{Franco2002ToricDS,
  title={Toric duality, Seiberg duality and Picard‐Lefschetz transformations},
  author={Sebasti'an Franco and Amihay Hanany},
  journal={Protein Science},
  year={2002},
  volume={51},
  pages={738-744}
}
Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a single node in the quiver forms a group which is contained in a larger group given by a set of Picard-Lefschetz transformations. This leads to elements in the group (sometimes called fractional Seiberg Duals) which are not Seiberg Duality on a single node, thus… Expand

Figures from this paper

Master space, Hilbert series and Seiberg duality
We analyze the action of Toric (Seiberg) duality on the combined mesonic and baryonic moduli space of quiver gauge theories obtained from D3 branes at Calabi-Yau singularities. We analyze inExpand
Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
It is known that a 4d N = 1 SCFT lives on D3-branes probing a local del Pezzo Calabi-Yau singularity. The Seiberg (or toric) duality of this SCFT arises from the Picard-Lefshetz transformation of theExpand
Seiberg duality as derived equivalence for some quiver gauge theories
We study Seiberg duality of quiver gauge theories associated to the complex cone over the second del Pezzo surface. Homomorphisms in the path algebra of the quivers in each of these cases satisfyExpand
Duality walls, duality trees and fractional branes
We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in theExpand
On the fate of tachyonic quivers
We study gauge theories on the world-volume of D3-branes probing singularities. Seiberg duality can be realized as a sequence of Picard-Lefschetz monodromies on 3-cycles in the mirror manifold. InExpand
A trio of dualities: Walls, trees and cascades
We study the RG flow of N = 1 world-volume gauge theories of D3-brane probes on certain singular Calabi-Yau threefolds. Taking the gauge theories out of conformality by introducing fractional branes,Expand
N-ification of forces: a holographic perspective on D-brane model building
We study geometric aspects of extensions of the supersymmetric standard model that exhibit a periodic duality cascade. Via the holographic correspondence, the growth of the gauge group rank towardsExpand
Chaotic duality in string theory
We investigate the general features of renormalization group flows near superconformal fixed points of four dimensional N=1 supersymmetric gauge theories with gravity duals. The gauge theories weExpand
Brane Tilings, M2-branes and Orbifolds
Brane Tilings represent one of the largest classes of superconformal theories with known gravity duals in 3+1 and also 2+1 dimensions. They provide a useful link between a large class of quiver gaugeExpand
Phases of M2-brane theories
We investigate different toric phases of 2+1 dimensional quiver gauge theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane tiling for each toric phase is presented. We apply theExpand
...
1
2
3
...

References

SHOWING 1-10 OF 17 REFERENCES
Toric duality as Seiberg duality and brane diamonds
We use fleld theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality for N = 1 theories with toric moduli spaces. This resolves the puzzle concerning the physicalExpand
Quiver theories, soliton spectra and Picard-Lefschetz transformations
Quiver theories arising on D3-branes at orbifold and del Pezzo singularities are studied using mirror symmetry. We show that the quivers for the orbifold theories are given by the soliton spectrum ofExpand
Phase structure of D-brane gauge theories and toric duality
Harnessing the unimodular degree of freedom in the definition of any toric diagram, we present a method of constructing inequivalent gauge theories which are world-volume theories of D-branes probingExpand
Symmetries of Toric Duality
This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality willExpand
Geometric dualities in 4d field theories and their 5d interpretation
We study four-dimensional = 1 gauge theories arising on D3-branes probing toric singularities. Toric dualities and flows between theories corresponding to different singularities are analyzed byExpand
Toric duality is Seiberg duality
We study four N = 1 SU(N) 6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of NExpand
Quiver theories from D6 branes via mirror symmetry
We study = 1 four dimensional quiver theories arising on the worldvolume of D3-branes at del Pezzo singularities of Calabi-Yau threefolds. We argue that under local mirror symmetry D3-branes becomeExpand
Branes and toric geometry
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.Expand
Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes
We investigate orientifolds of type II string theory on K3 and Calabi-Yau 3-folds with intersecting D-branes wrapping special lagrangian cycles. We determine quite generically the chiral masslessExpand
Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams
We continue to study 5d N = 1 supersymmetric field theories and their compactifications on a circle through brane configurations. We develop a model, which we call (p,q) Webs, which enables simpleExpand
...
1
2
...