729 research outputs found
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 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
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
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.
Phase structure of lattice QCD for general number of flavors
We investigate the phase structure of lattice QCD for the general number of
flavors in the parameter space of gauge coupling constant and quark mass,
employing the one-plaquette gauge action and the standard Wilson quark action.
Performing a series of simulations for the number of flavors --360 with
degenerate-mass quarks, we find that when there is a line of a bulk
first order phase transition between the confined phase and a deconfined phase
at a finite current quark mass in the strong coupling region and the
intermediate coupling region. The massless quark line exists only in the
deconfined phase. Based on these numerical results in the strong coupling limit
and in the intermediate coupling region, we propose the following phase
structure, depending on the number of flavors whose masses are less than
which is the physical scale characterizing the phase transition in
the weak coupling region: When , there is only a trivial IR fixed
point and therefore the theory in the continuum limit is free. On the other
hand, when , there is a non-trivial IR fixed point and
therefore the theory is non-trivial with anomalous dimensions, however, without
quark confinement. Theories which satisfy both quark confinement and
spontaneous chiral symmetry breaking in the continuum limit exist only for .Comment: RevTeX, 20 pages, 43 PS figure
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
Funding the Children's Act: assessing the adequacy of the 2011/12 budgets of the provincial departments of social development
An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories
An algebraic criterion for the vanishing of the beta function for
renormalizable quantum field theories is presented. Use is made of the descent
equations following from the Wess-Zumino consistency condition. In some cases,
these equations relate the fully quantized action to a local gauge invariant
polynomial. The vanishing of the anomalous dimension of this polynomial enables
us to establish a nonrenormalization theorem for the beta function ,
stating that if the one-loop order contribution vanishes, then will
vanish to all orders of perturbation theory. As a by-product, the special case
in which is only of one-loop order, without further corrections, is
also covered. The examples of the N=2,4 supersymmetric Yang-Mills theories are
worked out in detail.Comment: 1+32 pages, LaTeX2e, typos correcte
Reduction of Couplings in Quantum Field Theories with applications in Finite Theories and the MSSM
We apply the method of reduction of couplings in a Finite Unified Theory and
in the MSSM. The method consists on searching for renormalization group
invariant relations among couplings of a renormalizable theory holding to all
orders in perturbation theory. It has a remarkable predictive power since, at
the unification scale, it leads to relations between gauge and Yukawa couplings
in the dimensionless sectors and relations involving the trilinear terms and
the Yukawa couplings, as well as a sum rule among the scalar masses and the
unified gaugino mass in the soft breaking sector. In both the MSSM and the FUT
model we predict the masses of the top and bottom quarks and the light Higgs in
remarkable agreement with the experiment. Furthermore we also predict the
masses of the other Higgses, as well as the supersymmetric spectrum, both being
in very confortable agreement with the LHC bounds on Higgs and supersymmetric
particles.Comment: 18 pages, 4 figures. To appear in the proceedings of LT-10, Varna.
Based on invited talks given at: LT-10, Varna; PACT-2013, Madrid; SQS'2013,
Dubna; CORFU 2013, Corfu, and in several invited seminar
Wilsonian Matching of Effective Field Theory with Underlying QCD
We propose a novel way of matching effective field theory with the underlying
QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive
Wilsonian matching conditions between current correlators obtained by the
operator product expansion in QCD and those by the hidden local symmetry (HLS)
model. This determines without much ambiguity the bare parameters of the HLS at
the cutoff scale in terms of the QCD parameters. Physical quantities for the pi
and rho system are calculated by the Wilsonian RGE's from the bare parameters
in remarkable agreement with the experiment.Comment: 13 pages, 4 figures, Minor corrections. This is the version to appear
in Physical Review
Bulk fields with general brane kinetic terms
We analyse the effect of general brane kinetic terms for bulk scalars,
fermions and gauge bosons in theories with extra dimensions, with and without
supersymmetry. We find in particular a singular behaviour when these terms
contain derivatives orthogonal to the brane. This is brought about by
divergences arising at second and higher order in perturbation
theory. We argue that this behaviour can be smoothed down by classical
renormalization.Comment: 31 pages, v2 few typos correcte
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