Mass Deformed Exact S-parameter in Conformal Theories

We use the exact expression for the S parameter in the perturbative region of the conformal window to establish its dependence on the explicit introduction of fermion masses. We demonstrate that the relative ordering with which one sends to zero either the fermion mass or the external momentum leads to drastically different limiting values of S. Our results apply to any fermion matter representation and can be used as benchmark for the determination of certain relevant properties of the conformal window of any generic vector like gauge theory with fermionic matter. We finally suggest the existence of a universal lower bound on the opportunely normalized S parameter and explore its theoretical and phenomenological implications. Our exact results constitute an ideal framework to correctly interpret the lattice studies of the conformal window of strongly interacting theories.Comment: 4 pages, 2 figures. 2column

Nonperturbative Results for Yang-Mills Theories

Some non perturbative aspects of the pure SU(3) Yang-Mills theory are investigated assuming a specific form of the beta function, based on a recent modification by Ryttov and Sannino of the known one for supersymmetric gauge theories. The characteristic feature is a pole at a particular value of the coupling constant, g. First it is noted, using dimensional analysis, that physical quantities behave smoothly as one travels from one side of the pole to the other. Then it is argued that the form of the integrated beta function g(m), where m is the mass scale, determines the mass gap of the theory. Assuming the usual QCD value one finds it to be 1.67 GeV, which is in surprisingly good agreement with a quenched lattice calculation. A similar calculation is made for the supersymmetric Yang-Mills theory where the corresponding beta function is considered to be exact.Comment: RevTeX, 2colmuns, 6 pages and 7 figure

QCD Dual

We uncover a novel solution of the 't Hooft anomaly matching conditions for QCD. Interestingly in the perturbative regime the new gauge theory, if interpreted as a possible QCD dual, predicts the critical number of flavors above which QCD in the nonperturbative regime, develops an infrared stable fixed point. Remarkably this value is identical to the maximum bound predicted in the nonpertubative regime via the all-orders conjectured beta function for nonsupersymmetric gauge theories.Comment: RevTeX, 13 pages. Added discussion on operator matching and flavor decoupling. Version to match the published on

Large N Scalars: From Glueballs to Dynamical Higgs Models

We construct effective Lagrangians, and corresponding counting schemes, valid to describe the dynamics of the lowest lying large N stable massive composite state emerging in strongly coupled theories. The large N counting rules can now be employed when computing quantum corrections via an effective Lagrangian description. The framework allows for systematic investigations of composite dynamics of non-Goldstone nature. Relevant examples are the lightest glueball states emerging in any Yang-Mills theory. We further apply the effective approach and associated counting scheme to composite models at the electroweak scale. To illustrate the formalism we consider the possibility that the Higgs emerges as: the lightest glueball of a new composite theory; the large N scalar meson in models of dynamical electroweak symmetry breaking; the large N pseudodilaton useful also for models of near-conformal dynamics. For each of these realisations we determine the leading N corrections to the electroweak precision parameters. The results nicely elucidate the underlying large N dynamics and can be used to confront first principle lattice results featuring composite scalars with a systematic effective approach.Comment: 15 pages ReVTeX, 3 figure

Color Superconductivity: Symmetries and Effective Lagrangians

I briefly review the symmetries and the associated low energy effective Lagrangian for two light flavor Color Superconductivity (2SC).Comment: 6 pages, AIP format. Talk given at QCD@work conference, Martina Franca, Italy, 16-20 Jun 200

Chiral Phase Transition for SU(N) Gauge Theories

We describe the chiral phase transition for vector-like SU(N) gauge theories as a function of the number of quark flavors Nf by making use of an anomaly-induced effective potential. The potential depends explicitly on the full beta-function and the anomalous dimension \gamma of the quark mass operator. By using this potential we argue that chiral symmetry is restored for \gamma <1. A perturbative computation of \gamma then leads to an estimate of the critical value Nf^c for the transition.Comment: 7 pages, LaTeX AIP style. Conf. Proc. "New Directions in Quantum Chromodynamics

Magnetic S-parameter

We propose a direct test of the existence of gauge duals for nonsupersymmetric asymptotically free gauge theories developing an infrared fixed point by computing the S-parameter in the electric and dual magnetic description. In particular we show that at the lower bound of the conformal window the magnetic S-parameter, i.e. the one determined via the dual magnetic gauge theory, assumes a simple expression in terms of the elementary magnetic degrees of freedom. The results further support our recent conjecture of the existence of a universal lower bound on the S parameter and indicates that it is an ideal operator for counting the active physical degrees of freedom within the conformal window. Our results can be directly used to unveil possible four dimensional gauge duals and constitute the first explicit computation of a nonperturbative quantity, in the electric variables, via nonsupersymmetric gauge duality.Comment: RevTeX 4, 4 pages, two columns. Version to match the published version in Phys. Rev. Let

From Super QCD to QCD

We present a ``toy'' model for breaking supersymmetric gauge theories at the effective Lagrangian level. We show that it is possible to achieve the decoupling of gluinos and squarks, below a given supersymmetry breaking scale m, in the fundamental theory for super QCD once a suitable choice of supersymmetry breaking terms is made. A key feature of the model is the description of the ordinary QCD degrees of freedom via the auxiliary fields of the supersymmetric effective Lagrangian. Once the anomaly induced effective QCD meson potential is deduced we also suggest a decoupling procedure, when a flavored quark becomes massive, which mimics the one employed by Seiberg for supersymmetric theories. It is seen that, after quark decoupling, the QCD potential naturally converts to the one with one less flavor. Finally we investigate the N_c and N_f dependence of the \eta^{\prime} mass.Comment: Contribution to the proceedings of the MRST-98 meeting. 9 pages, RevTe