Duality and Superconvergence Relation in Supersymmetric Gauge Theories

We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.Comment: 20 pages, LaTe

Analytic Approach to Perturbative QCD

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.Comment: Latex-file, 19 pages, 2 tables, 51 references, to be published in Int. J. Mod. Phys.

The Riemann Surface of a Static Dispersion Model and Regge Trajectories

The S-matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy $\omega$ in the plane with cuts $(-\infty,-1],[+1,+\infty)$. In the elastic case it reduces to N functions $S_{i}(\omega)$ connected by the crossing symmetry matrix A. The scattering of a neutral pseodoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). The Regge trajectories of this model are explicitly found.Comment: 5 pages, LaTe

Infinite reduction of couplings in non-renormalizable quantum field theory

I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the irrelevant terms as unique functions of a reduced set of independent couplings lambda, such that the divergences are removed by means of field redefinitions plus renormalization constants for the lambda's. I consider non-renormalizable theories whose renormalizable subsector R is interacting and does not contain relevant parameters. The "infinite" reduction is determined by i) perturbative meromorphy around the free-field limit of R, or ii) analyticity around the interacting fixed point of R. In general, prescriptions i) and ii) mutually exclude each other. When the reduction is formulated using i), the number of independent couplings remains finite or slowly grows together with the order of the expansion. The growth is slow in the sense that a reasonably small set of parameters is sufficient to make predictions up to very high orders. Instead, in case ii) the number of couplings generically remains finite. The infinite reduction is a tool to classify the irrelevant interactions and address the problem of their physical selection.Comment: 40 pages; v2: more explanatory comments; appeared in JHE

Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory

Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills theory.Comment: 4 pages, no figures; version to be published in Physical Review Letter

Quarkonia in Hamiltonian Light-Front QCD

A constituent parton picture of hadrons with logarithmic confinement naturally arises in weak coupling light-front QCD. Confinement provides a mass gap that allows the constituent picture to emerge. The effective renormalized Hamiltonian is computed to ${\cal O}(g^2)$, and used to study charmonium and bottomonium. Radial and angular excitations can be used to fix the coupling $\alpha$, the quark mass $M$, and the cutoff $\Lambda$. The resultant hyperfine structure is very close to experiment.Comment: 9 pages, 1 latex figure included in the text. Published version (much more reader-friendly); corrected error in self-energ

On the infrared freezing of perturbative QCD in the Minkowskian region

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [1] it is claimed that infrared freezing can be proved also for Borel resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [2]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [1]. We discuss the arguments given in [1] and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.Comment: 19 pages, 1 figur

Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD

We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it. The renormalization procedure is designed to produce a Hamiltonian that will yield physical states that rapidly converge in an expansion in free-particle Fock-space sectors. To make this possible, we use light-front field theory to isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to force its free-state matrix elements to quickly decrease as the difference of the free masses of the states increases. The cutoff violates a number of physical principles of light-front pure-glue QCD, including Lorentz covariance and gauge covariance. This means that the operators in the Hamiltonian are not required to respect these physical principles. However, by requiring the Hamiltonian to produce cutoff-independent physical quantities and by requiring it to respect the unviolated physical principles of pure-glue QCD, we are able to derive recursion relations that define the Hamiltonian to all orders in perturbation theory in terms of the running coupling. We approximate all physical states as two-gluon states, and use our recursion relations to calculate to second order the part of the Hamiltonian that is required to compute the spectrum. We diagonalize the Hamiltonian using basis-function expansions for the gluons' color, spin, and momentum degrees of freedom. We examine the sensitivity of our results to the cutoff and use them to analyze the nonperturbative scale dependence of the coupling. We investigate the effect of the dynamical rotational symmetry of light-front field theory on the rotational degeneracies of the spectrum and compare the spectrum to recent lattice results. Finally, we examine our wave functions and analyze the various sources of error in our calculation.Comment: 75 pages, 17 figures, 1 tabl

Baryonic Regge trajectories with analyticity constraints

A model for baryonic Regge trajectories compatible with the threshold behavior required by unitarity and asymptotic behavior in agreement with analyticity constraints is given in explicit form. Widths and masses of the baryonic resonances on the N and $\Delta$ trajectories are reproduced. The MacDowell symmetry is exploited and an application is given.Comment: 12 pages, 6 figure

The High-Temperature Phase of Landau-Gauge Yang-Mills Theory

The properties of the high-temperature phase of Yang-Mills theory in Landau gauge are investigated by extending an earlier study on the infinite-temperature limit to finite temperatures. To this end the Dyson-Schwinger equations for the propagators of the gluon and the Faddeev-Popov ghost are solved analytically in the infrared and numerically at non-vanishing momenta. Gluons, polarized transversely with respect to the heat bath are found to comply with the Gribov-Zwanziger and the Kugo-Ojima scenario, while longitudinally polarized gluons are screened. Therefore the high-temperature phase is strongly interacting. It is furthermore conjectured that Yang-Mills theory undergoes a first-order phase transition. Indications are found that at high temperatures the thermodynamic properties are nearly those of an ideal gas, although long-range interactions prevail.Comment: 15 pages, 6 figures. Two paragraphs modified for clarification, some references added, three minor changes; in v3: typos corrected, version to appear in EPJ