Parameter Space of Quiver Gauge Theories

We initiate a systematic study of 2d (0,2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theor...

In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $\mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its ...

We explain how to construct a large class of new quiver gauge theories from branes at singularities by orientifolding and Higgsing old examples. The new models include the MSSM, decoupled from gravity, as well as some classic models of dynamical SUSY breaking. We also discuss topological criteria for unification.

In this paper we advance the program of using exceptional collections to understand the gauge theory description of a D-brane probing a Calabi-Yau singularity. To this end, we strengthen the connection between strong exceptional collections and fractional branes. To demonstrate our ideas, we derive a strong exceptional collection for every Y^{p,q} singularity, and also prove that this collection is simple.

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the $Y^{2,1}$ quiver gauge theory corresponding to a cone over the first del Pezzo surface, $dP_1$. This setup can be analyzed using ordinary supersymmetric field theory ...

We use large N duality to study brane/anti-brane configurations on a class of Calabi-Yau manifolds. With only branes present, the Calabi-Yau manifolds in question give rise to N=2 ADE quiver theories deformed by superpotential terms. We show that the large N duality conjecture of hep-th/0610249 reproduces correctly the known qualitative features of the brane/anti-brane physics. In the supersymmetric case, the gauge theories have Seiberg dualities which are represented as flop...

We engineer a class of quiver gauge theories with several interesting features by studying D-branes at a simple Calabi-Yau singularity. At weak 't Hooft coupling we argue using field theory techniques that these theories admit both supersymmetric vacua and meta-stable non-supersymmetric vacua, though the arguments indicating the existence of the supersymmetry breaking states are not decisive. At strong 't Hooft coupling we find simple candidate gravity dual descriptions for b...

We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In pa...

We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We de...

We study the relation between exactly marginal deformations in a large class of N=1 superconformal quiver gauge theories described by brane tilings and the degrees of freedom in the corresponding 5-brane systems. We show, with the help of NSVZ exact beta functions, that there are generically d-1 complex exactly marginal deformations of a gauge theory, where d is the perimeter of the corresponding n it, and the other two, the diagonal gauge coupling and a beta-like deformation...