In this paper we make further refinements to the duality proposed between N=1 SQCD and certain string (supergravity plus branes) backgrounds, working in the regime of comparable large number of colors and flavors. Using the string theory solutions, we predict different field theory observables and phenomena like Seiberg duality, gauge coupling and its running, the behavior of Wilson and 't Hooft loops, anomalous dimensions of the quark superfields, quartic superpotential coupling and its running, continuous and discrete anomaly matching. We also give evidence for the smooth interpolation between the Higgs and confining vacua. We provide several matchings between field theory and string theory computations.

In this note we describe how N=1 SQCD-like theories with a large number of flavors can be given a dual description in terms of a string background containing a large number of additional D5-branes. The dual geometries account for the backreaction of the additional branes: they depend on the ratio between the number of flavors and colors of the gauge theory. This note is based on hep-th/0602027. We present here also a new set of solutions, which are not included in the original paper.

We consider a general framework to study holographically the dynamics of fundamental quarks in a confining gauge theory. Flavors are introduced by placing a set of (coincident) branes and antibranes on a background dual to a confining color theory. The spectrum contains an open string tachyon and its condensation describes the U(Nf)L×U(Nf)R→U(Nf)V symmetry breaking. By studying worldvolume gauge transformations of the flavor brane action, we obtain the QCD global anomalies and an IR condition that allows to fix the quark condensate in terms of the quark mass. We find the expected Nf2 Goldstone bosons (for mq=0), the Gell-Mann–Oakes–Renner relation (for mq small) and the η′ mass. Remarkably, the linear confinement behavior for the masses of highly excited spin-1 mesons, mn2∼n is naturally reproduced.

We construct supergravity plus branes solutions, which we argue to be related to 4d $\mathcal{N}=1$ SQCD with a quartic superpotential. The geometries depend on the ratio ${N}_{f}/{N}_{c}$ which can be kept of order one, present a good singularity at the origin, and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like $R$-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings, and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members of a family of supergravity solutions dual to (unflavored) $\mathcal{N}=1$ SYM plus some UV completion.

The two-derivative approximation to non-critical strings is used as a qualitative tool to find solutions dual to four dimensional CFTs with matter in the fundamental. Two solutions are discussed: an AdS(5) X (S) over tilde (3) which is dual to an N = 1 SCFT only for a ratio of N-f/N-c and an AdS5 which is proposed to be dual to N = 0 QCD Nc in the conformal window. All solutions have curvatures of the order of the string scale. This contribution is based on [1]. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like R-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members of a family of supergravity solutions dual to (unflavored) N=1 SYM plus some UV completion.

We discuss the incorporation of quarks in the fundamental representation of the color group into the non-critical string/gauge duality. We focus on confining theories and address this question using two different approaches: (i) by introducing flavor probe branes and (ii) by deriving backreacted flavored near extremal gravity backgrounds. In the former approach we analyze the near extremal AdS(6) model with D-4 and anti-D-4 probe flavor branes included. We study the meson spectrum and discuss the role played by the constituent quark mass, related to the integration constant that defines the embedding. As for the second approach we derive a class of flavored AdS(n+1) x S-k black hole solutions. In particular we write down the flavored AdS(6) and AdS(5) black holes and the near extremal AdS(5) x S-1 backgrounds. We analyze several gauge dynamical properties associated with these models.

We find non-critical string backgrounds in five and eight dimensions, holographically related to four-dimensional conformal field theories with N=0 and N=1 supersymmetries. In the five-dimensional case we find an AdS_5 background metric for a string model related to non-supersymmetric, conformal QCD with large number of colors and flavors and discuss the conjectured existence of a conformal window from the point of view of our solution. In the eight-dimensional string theory, we build a family of solutions of the form AdS_5 x \tilde{S}^3 with \tilde{S}^3 a squashed three-sphere. For a special value of the ratio N_f/N_c, the background can be interpreted as the supersymmetric near-horizon limit of a system of color and flavor branes on R^{1,3} times a known four-dimensional generalization of the cigar. The N=1 dual theory with fundamental matter should have an IR fixed point only for a fixed ratio N_f/N_c. General features of the string/gauge theory correspondence for theories with fundamental flavors are also addressed.

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.

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.

We extend the BMN duality between IIB superstring theory on a pp-wave background and a sector of N=4 super Yang-Mills theory to the non-supersymmetric and unstable background built by Romans as a compactification on a U(1) bundle over CP2 with 3-form and 5-form field strength fluxes. We obtain a stable theory with the fewest number of supercharges (e.g. 16) allowed by this kind of solutions and make conjectures on the dual gauge theory.