Toric duality is Seiberg duality

Beasley, Chris; Plesser, M. Ronen

doi:10.1088/1126-6708/2001/12/001

Cited by 147 publications

(261 citation statements)

References 24 publications

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“…Furthermore, Seiberg duality is well-understood in the context of the toric quiver gauge theories [49,50,51]. We would like to study whether one can understand Seiberg duality for D-branes in these almost toric spaces [52,53,54] microscopically, as in [55,56].…”

Section: Discussionmentioning

confidence: 99%

Non-compact Gepner models, Landau-Ginzburg orbifolds and mirror symmetry

Ashok

Benichou

Troost

2008

J. High Energy Phys.

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We study non-compact Gepner models that preserve sixteen or eight supercharges in type II string theories. In particular, we develop an orbifolded Landau-Ginzburg description of these models analogous to the Landau-Ginzburg formulation of compact Gepner models. The Landau-Ginzburg description provides an easy and direct access to the geometry of the singularity associated to the non-compact Gepner models. Using these tools, we are able to give an intuitive account of the chiral rings of the models, and of the massless moduli in particular. By studying orbifolds of the singular linear dilaton models, we describe mirror pairs of non-compact Gepner models by suitably adapting the Greene-Plesser construction of mirror pairs for the compact case. For particular models, we take a large level, low curvature limit in which we can analyze corrections to a flat space orbifold approximation of the non-compact Gepner models. This gives rise to a counting of moduli which differs from the toric counting in a subtle way.

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Section: Discussionmentioning

confidence: 99%

Non-compact Gepner models, Landau-Ginzburg orbifolds and mirror symmetry

Ashok

Benichou

Troost

2008

J. High Energy Phys.

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“…The complex cones over the zeroth Hirzebruch surface and the second del Pezzo surface arising from such partial resolutions each gives rise to a pair of toric dual theories [9,11,16]. The complex cone over the third del Pezzo surface, arising from another set of partial resolutions of C 3 /Z 3 × Z 3 gives rise to four toric dual theories instead [11,10]. We shall summarise the rules for obtaining toric dual theories in the next section.…”

Section: Jhep02(2004)070mentioning

confidence: 99%

“…This can thus be used to map the deformations of one theory to that of the other in such JHEP02 (2004)070 a way that the low-energy (IR) properties of the pair remain unaltered. Let us briefly recall how this works [10]. Starting with a quiver gauge theory one chooses a factor in the gauge group G, say SU(N c (i 0 )), corresponding to a node i 0 in the quiver.…”

Section: Seiberg Duality Of Quiver Gauge Theoriesmentioning

confidence: 99%

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Seiberg duality as derived equivalence for some quiver gauge theories

Mukhopadhyay

Ray

2004

J. High Energy Phys.

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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 satisfy relations which follow from a superpotential of the corresponding gauge theory as F-flatness conditions. We verify that Seiberg duality between each pair of these theories can be understood as a derived equivalence between the categories of modules of representation of the path algebras of the quivers. Starting from the projective modules of one quiver we construct tilting complexes whose endomorphism algebra yields the path algebra of the dual quiver. Finally, we present a general scheme for obtaining Seiberg dual quiver theories by constructing quivers whose path algebras are derived equivalent. We also discuss some combinatorial relations between this approach and some of the other approaches which has been used to study such dualities.

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“…As field theories, a natural question that arises in this context is the interplay between the existence of a finite Heisenberg group and Seiberg duality. Seiberg duality is an equivalence between two gauge theories [6], and has been extensively studied in the context of quiver gauge theories [7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Finite Heisenberg groups and Seiberg dualities in quiver gauge theories

et al. 2006

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A large class of quiver gauge theories admits the action of finite Heisenberg groups of the form Heis(Z q × Z q ). This Heisenberg group is generated by a manifest Z q shift symmetry acting on the quiver along with a second Z q rephasing (clock) generator acting on the links of the quiver. Under Seiberg duality, however, the action of the shift generator is no longer manifest, as the dualized node has a different structure from before. Nevertheless, we demonstrate that the Z q shift generator acts naturally on the space of all Seiberg dual phases of a given quiver. We then prove that the space of Seiberg dual theories inherits the action of the original finite Heisenberg group, where now the shift generator Z q is a map among fields belonging to different Seiberg phases. As examples, we explicitly consider the action of the Heisenberg group on Seiberg phases for C 3 /Z 3 , Y 4,2 and Y 6,3 quiver.

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Toric duality is Seiberg duality

Cited by 147 publications

References 24 publications

Non-compact Gepner models, Landau-Ginzburg orbifolds and mirror symmetry

Non-compact Gepner models, Landau-Ginzburg orbifolds and mirror symmetry

Seiberg duality as derived equivalence for some quiver gauge theories

Finite Heisenberg groups and Seiberg dualities in quiver gauge theories

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