Quivers via anomaly chains

We study quivers in the context of matrix models. We introduce chains of generalized Konishi anomalies to write the quadratic and cubic equations that constrain the resolvents of general affine and non-affine quiver gauge theories, and give a procedure to calculate all higher-order relations. For these theories we also evaluate, as functions of the resolvents, VEV's of chiral operators with two and four bifundamental insertions. As an example of the general procedure we explicitly consider the two simplest quivers A2 and A1(affine), obtaining in the first case a cubic algebraic curve, and for the affine theory the same equation as that of U(N) theories with adjoint matter, successfully reproducing the RG cascade result.Comment: 32 pages, latex; typos corrected, published versio

Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models

We study the phases and geometry of the N=1 A_2 quiver gauge theory using matrix models and a generalized Konishi anomaly. We consider the theory both in the Coulomb and Higgs phases. Solving the anomaly equations, we find that a meromorphic one-form sigma(z)dz is naturally defined on the curve Sigma associated to the theory. Using the Dijkgraaf-Vafa conjecture, we evaluate the effective low-energy superpotential and demonstrate that its equations of motion can be translated into a geometric property of Sigma: sigma(z)dz has integer periods around all compact cycles. This ensures that there exists on Sigma a meromorphic function whose logarithm sigma(z)dz is the differential. We argue that the surface determined by this function is the N=2 Seiberg-Witten curve of the theory.Comment: 41 pages, 2 figures, JHEP style. v2: references adde

A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories

We study the spectrum of BPS domain walls within the parameter space of N=1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R^3 x S^1, we examine the wall spectrum by combining direct calculations at special points in the parameter space with insight drawn from the leading order potential between minimal walls, i.e those interpolating between adjacent vacua. We show that the multiplicity of composite BPS walls -- as characterised by the CFIV index -- exhibits discontinuities on marginal stability curves within the parameter space of the maximally confining branch. The structure of these marginal stability curves for large N appears tied to certain singularities within the matrix model description of the confining vacua.Comment: 33 pages, LaTeX, 6 eps figures; v2: references adde

A-D-E Quivers and Baryonic Operators

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The string theory analysis predicts that the number and the order of the fixed points of Gamma acting on S^2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by developing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks. We also find that the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1, references adde

N = 1 geometries via M-theory

We provide an M-theory geometric set-up to describe four-dimensional N = 1 gauge theories. This is realized by a generalization of Hitchin’s equation. This framework encompasses a rich class of theories including superconformal and confining ones. We show how the spectral data of the generalized Hitchin’s system encode the infrared properties of the gauge theory in terms of N = 1 curves. For N = 1 deformations of N = 2 theories in class S, we show how the superpotential is encoded in an appropriate choice of boundary conditions at the marked points in different S-duality frames. We elucidate our approach in a number of cases — including Argyres-Douglas points, confining phases and gaugings of T_N theories — and display new results for linear and generalized quivers

Amplitudes With Different Helicity Configurations Of Noncommutative QED

The amplitudes of purely photonic and photon{2-fermion processes of non- commutative QED (NCQED) are derived for different helicity configurations of photons. The basic ingredient is the NCQED counterpart of Yang-Mills recursion relations by means of Berends and Giele. The explicit solutions of recursion relations for NCQED photonic processes with special helicity configurations are presented.Comment: 23 pages, 2 figure

Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory

We study the half-BPS mesonic chiral ring of the N=1 superconformal quiver theories arising from N D3-branes stacked at Y^pq and L^abc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry. This map enables us to write a partition function at finite N over mesonic half-BPS states. It agrees with the bulk gravity interpretation of chiral ring states as cohomologically trivial giant gravitons. The quiver theories for L^aba, which have singular base geometries, contain extra operators not counted by the naive bulk partition function. These extra operators have a natural interpretation in terms of twisted states localized at the orbifold-like singularities in the bulk.Comment: Latex, 25pgs, 12 figs, v2: minor clarification

Color superconductivity, Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories

We study the Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories. In order to do that we consider an N=4 super Yang-Mills theory with an arbitrary gauge group G and add some N=2, N=1 and N=0 deformation terms. We analyze some possible vacuum solutions and phases of the theory, depending on the deformation terms which are added. In the Coulomb phase for the N=2* theory, G is broken to U(1)^r and the theory has monopole solutions. Then, by adding some deformation terms, the theory passes to the Higgs or color superconducting phase, in which G is broken to its center C_G. In this phase we construct the Z_N flux tubes ansatz and obtain the BPS string tension. We show that the monopole magnetic fluxes are linear integer combinations of the string fluxes and therefore the monopoles can become confined. Then, we obtain a bound for the threshold length of the string-breaking. We also show the possible formation of a confining system with 3 different monopoles for the SU(3) gauge group. Finally we show that the BPS string tensions of the theory satisfy the Casimir scaling law.Comment: 18 pages, 2 figures, typo corrections. Version to appear in Phys. Rev.

Aspects of ABJM orbifolds with discrete torsion

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order $m$ of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of $m$ in addition to the other effects that were found before in the literature. Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian