Littérature scientifique sur le sujet « Superconformal QCD »

The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion q q ¯ eigenstate has zero mass for m q = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS 5 space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

Dynamics of π, K-mesons interactions is formulated in terms of composite superconformal string model. Supersymmetry is defined on two-dimensional world surface only. Dimensionality of target space equals to four. The model treats usual hadron scale which is of order 1 GeV-2, as string scale α′. Intercept of leading meson trajectory equals to ½. Tree amplitudes are free from ghosts in physical state spectrum in accordance with usual classical superstring amplitudes. Interaction of π-mesons in the chiral limit in the model turns out in correspondence with description in terms of chiral Lagrangian for pions in QCD.

This talk begins with some history and basic facts about string theory and its connections with strong interactions. Comparisons of stacks of Dirichlet branes with curved backgrounds produced by them are used to motivate the AdS/CFT correspondence between superconformal gauge theory and string theory on a product of Anti-de Sitter space and a compact manifold. The ensuing duality between semi-classical spinning strings and long gauge theory operators is briefly reviewed. Strongly coupled thermal SYM theory is explored via a black hole in 5-dimensional AdS space, which leads to explicit results for its entropy and shear viscosity. A conjectured universal lower bound on the viscosity to entropy density ratio, and its possible relation to recent results from RHIC, are discussed. Finally, some available results on string duals of confining gauge theories are briefly reviewed.

The QCD light-front Hamiltonian equation HLFΨ=M2Ψ derived from quantization at fixed LF time τ=t + z/c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the qq¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and AdS5, if one modifies the AdS5 action by the dilaton eκ2z2 in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion qq¯ eigenstate has zero mass at mq=0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling αs(Q2)∝e-Q2/4κ2. The mass scale κ underlying hadron masses can be connected to the parameter ΛMS¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.

Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity — supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons: [Formula: see text] The dynamics of the superpartner hadrons also match; for example, the power-law fall-off of the form factors are the same for the mesonic and baryonic superpartners, in agreement with twist counting rules. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding superconformal quantum mechanics into AdS space. This procedure also generates a spin–spin interaction between the hadronic constituents. A specific breaking of conformal symmetry inside the graded algebra determines a unique quark-confining light-front potential for light hadrons in agreement with the soft-wall AdS/QCD approach and light-front holography. Only one mass parameter [Formula: see text] appears; it sets the confinement mass scale, a universal value for the slope of all Regge trajectories, the nonzero mass of the proton and other hadrons in the chiral limit, as well as the length scale which underlies their structure. The mass for the pion eigenstate vanishes in the chiral limit. When one includes the constituent quark masses using the Feynman–Hellman theorem, the predictions are consistent with the empirical features of the light-quark hadronic spectra. Our analysis can be consistently applied to the excitation spectra of the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] meson families as well as to the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass-squared of the light hadrons can be expressed in a universal and frame-independent decomposition of contributions from the constituent kinetic energy, the confinement potential, and spin–spin contributions. We also predict features of hadron dynamics, including hadronic light-front wave functions, distribution amplitudes, form factors, valence structure functions and vector meson electroproduction phenomenology. The mass scale [Formula: see text] can be connected to the parameter [Formula: see text] in the QCD running coupling by matching the nonperturbative dynamics, as described by the light-front holographic approach to the perturbative QCD regime. The result is an effective coupling defined at all momenta. The matching of the high and low momentum-transfer regimes determines a scale [Formula: see text] proportional to [Formula: see text] which sets the interface between perturbative and nonperturbative hadron dynamics. The use of [Formula: see text] to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the scheme-independent Principle of Maximal Conformality (PMC) procedure for setting renormalization scales, can greatly improve the precision of perturbative QCD predictions.

A primary question in hadron physics is how the mass scale for hadrons consisting of light quarks, such as the proton, emerges from the QCD Lagrangian even in the limit of zero quark mass. If one requires the effective action which underlies the QCD Lagrangian to remain conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory, then a unique, color-confining potential with a mass parameter [Formula: see text] emerges. The actual value of the parameter [Formula: see text] is not set by the model – only ratios of hadron masses and other hadronic mass scales are predicted. The result is a nonperturbative, relativistic light-front quantum mechanical wave equation, the Light-Front Schrödinger Equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the identical slope in the radial quantum number [Formula: see text] and orbital angular momentum [Formula: see text]. The same light-front equations for mesons with spin [Formula: see text] also can be derived from the holographic mapping to QCD (3+1) at fixed light-front time from the soft-wall model modification of AdS5 space with a specific dilaton profile. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. One can also extend the analysis to baryons using superconformal algebra – [Formula: see text] supersymmetric representations of the conformal group. The resulting fermionic LF bound-state equations predict striking similarities between the meson and baryon spectra. In fact, the holographic QCD light-front Hamiltonians for the states on the meson and baryon trajectories are identical if one shifts the internal angular momenta of the meson ([Formula: see text]) and baryon ([Formula: see text]) by one unit: [Formula: see text]. We also show how the mass scale [Formula: see text] underlying confinement and the masses of light-quark hadrons determines the scale [Formula: see text] controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The data for the effective coupling defined from the Bjorken sum rule [Formula: see text] are remarkably consistent with the Gaussian form predicted by LF holographic QCD. The result is an effective coupling defined at all momenta. The predicted value [Formula: see text] is in agreement with the world average [Formula: see text]. We thus can connect [Formula: see text] to hadron masses. The analysis applies to any renormalization scheme.

We discussed that for some particular nonsupersymmetric theories, a generalized symmetry that includes both the scale and axial transformations and leads to a single current may contain also a pseudoscalar term. The method, inspired by the superconformal anomalies, has important application for low-energy effective models where it allows the introduction of a single complex glueball field with a scalar and a pseudoscalar component on the same footing with the complex meson nonet fields made of quarks. Both axial and trace anomalies are satisfied in accordance to the meson structure and the QCD requirements.

This thesis is dedicated to the study of Wilson loops in supersymmetric gauge theories, we will study their properties and how they are related to physical observables, such as the Bremsstrahlung function that controls to the energy radiated by an accelerating particle. We will give various examples of the computation of their expectations values using perturbative and non-perturbative techniques. For SU(N) superconformal QCD we perform a three-loop calculation of the generalized cusp anomalous dimension of the BPS Wilson loop operator using HQET formalism. We obtain an expression which is valid at generic geometric and internal angles and finite gauge group rank N. For equal and opposite angles this expression vanishes, proving that at these points the cusp becomes BPS. From its small angle expansion we derive the corresponding Bremsstrahlung function at three loops, matching the matrix model prediction given in terms of derivatives of the Wilson loop on the ellipsoid.
This thesis is dedicated to the study of Wilson loops in supersymmetric gauge theories, we will study their properties and how they are related to physical observables, such as the Bremsstrahlung function that controls to the energy radiated by an accelerating particle. We will give various examples of the computation of their expectations values using perturbative and non-perturbative techniques. For SU(N) superconformal QCD we perform a three-loop calculation of the generalized cusp anomalous dimension of the BPS Wilson loop operator using HQET formalism. We obtain an expression which is valid at generic geometric and internal angles and finite gauge group rank N. For equal and opposite angles this expression vanishes, proving that at these points the cusp becomes BPS. From its small angle expansion we derive the corresponding Bremsstrahlung function at three loops, matching the matrix model prediction given in terms of derivatives of the Wilson loop on the ellipsoid.

Ce mémoire fait état des résultats obtenus concernant les vecteurs singuliers de l’algèbre superconforme dans le secteur de Ramond. Une formule explicite exprimant ces vecteurs singuliers a été obtenue en termes de superpolynômes de Jack via la représentation de l’algèbre superconforme en termes de superpolynômes symétriques. On présente d’abord les partitions d’entiers et les fonctions symétriques standards. Ceci permet d’introduire les fonctions propres du modèle Calogero-Sutherland (CS) en termes de polynômes de Jack qui se révèlent être une représentation efficace des vecteurs singuliers de l’algèbre conforme. Suivant cette piste, on procède à la supersymétrisation du modèle CS ce qui permet de générer les superpolynômes de Jack, polynômes symétriques dans le superespace. On présente finalement la formule explicite des vecteurs singuliers de l’algèbre superconforme en termes de superpolynômes de Jack.
This mémoire presents results concerning the Ramond singular vectors of the superconformal algebra. An explicit formula has been obtained for the Ramond singular vectors of the superconformal algebra via its superpolynomial representation and the formula is given here in terms of Jack superpolynomials. We first present some basic elements of the integer partition and symmetric functions theories. This leads us to consider the eigenfunctions of the Calogero-Sutherland (CS) model, the Jack polynomials. These happen to be the singular vectors of the conformal algebra when represented in terms of symmetric polynomials. Given those results, we extend the CS model to the supersymmetric case and interpret its eigenfunctions as the Jack superpolynomials which are symmetric functions in superspace. We then display the explicit formula of the Ramond singular vectors of the superconformal algebra which has been obtained in terms of Jack superpolynomials.