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We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge(More)
Gravity solutions dual to d-dimensional field theories at finite charge density have a near-horizon region which is AdS2 × Rd−1. The scale invariance of the AdS2 region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a (0+1)-dimensional CFT. This interpretation sheds light on recently-discovered(More)
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(More)
We describe a technique which enables one to quickly compute an infinite number of toric geometries and their dual quiver gauge theories. The central object in this construction is a “brane tiling,” which is a collection of D5-branes ending on an NS5-brane wrapping a holomorphic curve that can be represented as a periodic tiling of the plane. This(More)
Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3–branes probing a Calabi–Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of(More)
Brane tilings are efficient mnemonics for Lagrangians of N = 2 Chern-Simons-matter theories. Such theories are conjectured to arise on M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple modification of the Kasteleyn technique is described which is conjectured to compute the three dimensional toric diagram of the non-compact(More)
Recently, a new way of deriving the moduli space of quiver gauge theories that arise on the world– volume of D3–branes probing singular toric Calabi–Yau cones was conjectured. According to the proposal, the gauge group, matter content and tree–level superpotential of the gauge theory is encoded in a periodic tiling, the dimer graph. The conjecture provides(More)
We introduce new techniques based on brane tilings to investigate D3branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge theories living on the D-branes. Using the set of ideas in this paper one recovers essentially all orientifolded theories(More)
Gravity solutions dual to d-dimensional field theories at finite charge density have a near-horizon region which is AdS2 × Rd−1. The scale invariance of the AdS2 region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a (0+1)-dimensional CFT. This interpretation sheds light on recently-discovered(More)