Parameter Space of Quiver Gauge Theories

We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1 dimensional quiver gauge theory that describes the dynamics of the branes at low energies. The results of Kontsevich and Soibelman predict how the degeneracies change. We argue that Seiberg dualities of the quiver gauge theories, which change the basis of BPS states, correspond to crossing the "walls of the second kind." There is a large class of examples, including local del Pezzo surfaces, where th...

Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge grou...

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 theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with ...

We study N=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 become D6-branes wrapped on a three torus in the mirror manifold. The type IIB (p,q) 5-brane web description of the local del Pezzo, being closely related to the geometry of its mirror manifold, encodes the geometry of 3-cycles and is used to obtain gauge groups, quiver diagrams and the c...

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. 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 identif...

Deformation of N=2 quiver gauge theories by adjoint masses leads to fixed manifolds of N=1 superconformal field theories. We elaborate on the role of the complex three-form flux in the IIB duals to these fixed point theories, primarily using field theory techniques. We study the moduli space at a fixed point and find that it is either the two (complex) dimensional ALE space or three-dimensional generalized conifold, depending on the type of three-form flux that is present. We...

We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ with fluxes, where $X$ is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of Generalised Calabi-Yau manifolds: the cone over $X$ admits an integrable generalised complex structure in terms of which the BPS sector of the gauge theory can be described. The moduli spaces of the deformed toric N=1 gauge theories are studied on a...

We show how to construct the general action coupling (multi)instantons to gauge theories arising from branes probing arbitrary toric singularities. We give a general set of rules for how to construct such an action given the knowledge of the superpotential for the gauge theory. The main idea is to obtain the action by higgsing a theory whose instanton dynamics is known, namely an orbifold of N=4 super Yang-Mills. We find that the couplings of the fermionic zero-modes with the...

We study a class of 4D $\mathcal{N}=1$ supersymmetric GUT- type models in the framework of the Beasley-Heckman-Vafa theory. We first review general results on MSSM and supersymmetric GUT; and we describe useful tools on 4D quiver gauge theories in F- theory set up. Then we study the effective supersymmetric gauge theory in the 7-brane wrapping 4-cycles in F-theory on local elliptic CY4s based on a complex tetrahedral surface $\mathcal{T}$ and its blown ups $\mathcal{T}_{n}$. ...

We study the generalization of S-duality and Argyres-Seiberg duality for a large class of N=2 superconformal gauge theories. We identify a family of strongly interacting SCFTs and use them as building blocks for generalized superconformal quiver gauge theories. This setup provides a detailed description of the ``very strongly coupled'' regions in the moduli space of more familiar gauge theories. As a byproduct, we provide a purely four dimensional construction of N=2 theories...