Elaborations on the String Dual to N=1 SQCD

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 higgsed and confining vacua. We provide several matchings between field theory and string theory computations.Comment: 44 pages, 6 figures. References added, minor rewritings, published versio

N=1 SQCD-like theories with N_f massive flavors from AdS/CFT and beta functions

We study new supergravity solutions related to large-$N_c$ ${\cal N}=1$ supersymmetric gauge field theories with a large number $N_f$ of massive flavors. We use a recently proposed framework based on configurations with $N_c$ color D5 branes and a distribution of $N_f$ flavor D5 branes, governed by a function $N_f S(r)$. Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of $x\equiv N_f/N_c$. In the IR region, the solution smoothly approaches the deformed Maldacena-N\'u\~nez solution. In the UV region it approaches a linear dilaton solution. For $x<2$ the gauge coupling $\beta_g$ function computed holographically is negative definite, in the UV approaching the NSVZ $\beta$ function with anomalous dimension $\gamma_0= -1/2$ (approaching $-3/(32\pi^2)(2N_c-N_f)g^3$)), and with $\beta_g \to-\infty$ in the IR. For $x=2$, $\beta_g$ has a UV fixed point at strong coupling, suggesting the existence of an IR fixed point at a lower value of the coupling. We argue that the solutions with $x>2$ describe a "Seiberg dual" picture where $N_f-2N_c$ flips sign.Comment: 18 pages, 10 figure

Holographic QCD and Pion Mass

To realize massive pions, we study variations of the holographic model of massless QCD using the D4/D8/anti-D8 brane configuration proposed by Sakai and Sugimoto. We propose deformations which break the chiral symmetry explicitly and compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. We also argue a chiral perturbation corresponding to our deformation.Comment: 23pages, minor changes, references adde

Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves

Using matrix-model methods we study three different N=2 models: U(N) x U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg-Witten curves (and associated Seiberg-Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U(N) theories with symmetric or antisymmetric matter we use the modified matrix-model prescription for the gauge-coupling matrix discussed in ref. [hep-th/0303268]. Moreover, in the matrix model for the U(N) theory with antisymmetric matter, one is required to expand around a different vacuum than one would naively have anticipated. With these modifications of the matrix-model prescription, the results of this paper are in complete agreement with those of Seiberg-Witten theory obtained using M-theory methods.Comment: 40 pages; v2: reference added; v3: minor typo fixed; v4: clarifying footnote added; published versio

Chiral Condensate in Holographic QCD with Baryon Density

We consider the chiral condensate in the baryonic dense medium using the generalized Sakai-Sugimoto model. It is defined as the vacuum expectation value of open Wilson line that is proposed to be calculated by use of the area of world-sheet instanton. We evaluate it in confined as well as deconfined phase. In both phases, the chiral condensate has a minimum as a function of baryon density. In the deconfined phase, taking into account the chiral symmetry restoration, we classify the behavior of chiral condensate into three types. One can set the parameter of the theory such that the results, in low but sufficiently higher density, is in agreement with the expectation from QCD.Comment: 23 pages, 8 figure

Non-Perturbative Planar Equivalence and the Absence of Closed String Tachyons

We consider 'orbifold' and 'orientifold' field theories from the dual closed string theory side. We argue that a necessary condition for planar equivalence to hold is the absence of a closed string tachyonic mode in the dual non-supersymmetric string. We analyze several gauge theories on R3xS1. In the specific case of U(N) theories with symmetric/anti-symmetric fermions ('orientifold field theories') the relevant closed string theory is tachyon-free at large compactification radius (due to winding modes), but it develops a tachyonic mode below a critical radius. Our finding is with agreement with field theory expectations of a phase transition from a C-parity violating phase to a C-parity preserving phase as the compactification radius increases. In the case of U(N)xU(N) theories with bi-fundamental matter ('orbifold field theories') a tachyon is always present in the string spectrum, at any compactification radius. We conclude that on R4 planar equivalence holds for 'orientfiold field theories', but fails for 'orbifold field theories' daughters of N=4 SYM and suggest the same for daughters of N=1 SYM. We also discuss examples of SO/Sp gauge theories with symmetric/anti-symmetric fermions. In this case planar equivalence holds at any compactification radius -in agreement with the absence of tachyons in the string dual.Comment: 14 pages, Latex. 3 eps figures. v2: ref. added. v3: clarifying sentences added in the abstract and at the end of section 4. version accepted to JHE

Phases of N=1 USp(2N_c) Gauge Theories with Flavors

We studied the phase structures of N=1 supersymmetric USp(2N_c) gauge theory with N_f flavors in the fundamental representation as we deformed the N=2 supersymmetric QCD by adding the superpotential for adjoint chiral scalar field. We determined the most general factorization curves for various breaking patterns, for example, the two different breaking patterns of quartic superpotential. We observed all kinds of smooth transitions for quartic superpotential. Finally we discuss the intriguing role of USp(0) in the phase structure and the possible connection with observations made recently in hep-th/0304271 (Aganagic, Intriligator, Vafa and Warner) and in hep-th/0307063 (Cachazo).Comment: 61pp; Improved the presentation, references are added and to appear in PR

The holographic quantum effective potential at finite temperature and density

We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for studying the ground state of the theory, symmetry breaking patterns and phase transitions. We derive general formulae for the effective potential and apply them to determine the phase transition temperature and density in the scaling region.Comment: 27 page

Baryon charge from embedding topology and a continuous meson spectrum in a new holographic gauge theory

We study a new holographic gauge theory based on probe D4-branes in the background dual to D4-branes on a circle with antiperiodic boundary conditions for fermions. Field theory configurations with baryons correspond to smooth embeddings of the probe D4-branes with nontrivial winding around an S^4 in the geometry. As a consequence, physics of baryons and nuclei can be studied reliably in this model using the abelian Born-Infeld action. However, surprisingly, we find that the meson spectrum is not discrete. This is related to a curious result that the action governing small fluctuations of the gauge field on the probe brane is the five-dimensional Maxwell action in Minkowski space despite the non-trivial embedding of the probe brane in the curved background geometry.Comment: 24 pages, LaTeX, 10 figures, v4: previously ignored effects of coupling to RR-fields included, meson spectrum qualitatively changed, v5: journal versio