Quivers, tilings, branes and rhombi
By A. Hanany, David Vegh. 2005
255 citations recorded by the source corpus.
We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact manifold [1]. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/29abbc5b43515008700933c6d138373dba30bc2c
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Citations in the corpus
- Dimer models from mirror symmetry and quivering amoebae (2005, background): “living on a subset of the T3 world-volume of the D6-branes, and provides a concrete string theoretical framework for the previous combinatorial results relating dimer models and quiver gauge theories [9, 10, 30]. Here we have only discussed the topology of the D6-branes. From general arguments the s”
- Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “[25, 26, 27, 28, 29, 30] have resulted in the determination of families of gauge theories that are dual to the wider class of toric Sasaki–Einstein manifolds L [27, 31] (see also [32]).”
- N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, unknown): “Contents”
- Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “The 3 here, of course, correspond to the (5)Since we are studying BPS mesons, we may emphasize the relationship between the concept of the “extremal BPS meson” (introduced in [28]) and that of the “zig-zag path” in [21, 22, 24].”
- Tilings, Chern-Simons Theories and M2 Branes (2008, background): “A natural question is if all toric CalabiYau singularities arise in this way and how to find the inverse algorithm, that in 3+1 dimensions is developed in [48, 49, 50].”
- Chiral flavors and M2-branes at toric CY4 singularities (2009, background): “Given a toric CY3 singularity in type IIB and N D3-branes probing it, the dual SCFT in 3+1 dimensions can be generically found with the algorithm in [48] (see also [49]).”
- THE MASTER SPACE OF N=1 GAUGE THEORIES (2008, background): “Only lately it is realized that the correct way to think about toric geometry in the context of gauge theories is through the language of dimer models and brane tilings [6, 7].”
- A simple class of N = 3 gauge/gravity duals (2008, background): “The field theories can be engineered from a brane configuration; their geometry is summarized by a “hyperKähler toric fan” that can be read off easily from the relative angles of the branes.”
- Dimer models and the special McKay correspondence (2009, methodology): “A G ] 1 M ay 2 00 9 Dimer models and the special McKay correspondence Akira Ishii and Kazushi Ueda”
- Brane tilings and their applications (2008, methodology): “According to the conjecture by Hanany-Herzog-Vegh [239], we can construct full strong exceptional collection (E1, E2, . . . EN ) from brane tilings such that N⊕ i,j=1 Hom(Ei, Ej) ∼= CΓ→, (6.13) where CΓ→ is the path algebra for subquiver Γ→, as we have defined above.”
- On the noncommutative Donaldson-Thomas invariants arising from brane tilings (2008, unknown): “Rationality conjecture 19 References 20”
- Dimer models and cluster categories of Grassmannians (2013, methodology): “We modify the discussion after [ 2 , Rk 6.2] for the boundary case (see also [ 18 , § 3] for the dual case).”