138 research outputs found
Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
We generalize modern ideas about the duality between Wilson loops and
scattering amplitudes in =4 SYM to large-N (or quenched) QCD. We show
that the area-law behavior of asymptotically large Wilson loops is dual to the
Regge-Veneziano behavior of scattering amplitudes at high energies and fixed
momentum transfer, when quark mass is small and/or the number of particles is
large. We elaborate on this duality for string theory in a flat space,
identifying the asymptotes of the disk amplitude and the Wilson loop of large-N
QCD.Comment: REVTex, 6 pages, 1 figure; v3: refs added; v4pp. to appear in PR
Simplicial vs. Continuum String Theory and Loop Equations
We derive loop equations in a scalar matrix field theory. We discuss their
solutions in terms of simplicial string theory -- the theory describing
embeddings of two--dimensional simplicial complexes into the space--time of the
matrix field theory. This relation between the loop equations and the
simplicial string theory gives further arguments that favor one of the
statements of the paper hep-th/0407018. The statement is that there is an
equivalence between the partition function of the simplicial string theory and
the functional integral in a continuum string theory -- the theory describing
embeddings of smooth two--dimensional world--sheets into the space--time of the
matrix field theory in question.Comment: 6 page
Light-Cone Wilson Loops and the String/Gauge Correspondence
We investigate a \Pi-shape Wilson loop in N=4 super Yang--Mills theory, which
lies partially at the light-cone, and consider an associated open superstring
in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous
dimensions of conformal operators with large Lorentz spin and present an
explicit calculation in perturbation theory to order \lambda. We find the
minimal surface in the supergravity approximation, that reproduces the Gubser,
Klebanov and Polyakov prediction for the anomalous dimensions at large
\lambda=g_YM^2 N, and discuss its quantum-mechanical interpretation.Comment: 17pp., Latex, 4 figures; v.2: factors of 2 put righ
Higher Genus Correlators for the Complex Matrix Model
We describe an iterative scheme which allows us to calculate any multi-loop
correlator for the complex matrix model to any genus using only the first in
the chain of loop equations. The method works for a completely general
potential and the results contain no explicit reference to the couplings. The
genus contribution to the --loop correlator depends on a finite number
of parameters, namely at most . We find the generating functional
explicitly up to genus three. We show as well that the model is equivalent to
an external field problem for the complex matrix model with a logarithmic
potential.Comment: 17 page
Schwinger-Dyson operator of Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra
We consider large-N multi-matrix models whose action closely mimics that of
Yang-Mills theory, including gauge-fixing and ghost terms. We show that the
factorized Schwinger-Dyson loop equations, expressed in terms of the generating
series of gluon and ghost correlations G(xi), are quadratic equations S^i G = G
xi^i G in concatenation of correlations. The Schwinger-Dyson operator S^i is
built from the left annihilation operator, which does not satisfy the Leibnitz
rule with respect to concatenation. So the loop equations are not differential
equations. We show that left annihilation is a derivation of the graded shuffle
product of gluon and ghost correlations. The shuffle product is the point-wise
product of Wilson loops, expressed in terms of correlations. So in the limit
where concatenation is approximated by shuffle products, the loop equations
become differential equations. Remarkably, the Schwinger-Dyson operator as a
whole is also a derivation of the graded shuffle product. This allows us to
turn the loop equations into linear equations for the shuffle reciprocal, which
might serve as a starting point for an approximation scheme.Comment: 13 pages, added discussion & references, title changed, minor
corrections, published versio
Center-stabilized Yang-Mills theory: confinement and large volume independence
We examine a double trace deformation of SU(N) Yang-Mills theory which, for
large and large volume, is equivalent to unmodified Yang-Mills theory up to
corrections. In contrast to the unmodified theory, large volume
independence is valid in the deformed theory down to arbitrarily small volumes.
The double trace deformation prevents the spontaneous breaking of center
symmetry which would otherwise disrupt large volume independence in small
volumes. For small values of , if the theory is formulated on with a sufficiently small compactification size , then an analytic
treatment of the non-perturbative dynamics of the deformed theory is possible.
In this regime, we show that the deformed Yang-Mills theory has a mass gap and
exhibits linear confinement. Increasing the circumference or number of
colors decreases the separation of scales on which the analytic treatment
relies. However, there are no order parameters which distinguish the small and
large radius regimes. Consequently, for small the deformed theory provides
a novel example of a locally four-dimensional pure gauge theory in which one
has analytic control over confinement, while for large it provides a simple
fully reduced model for Yang-Mills theory. The construction is easily
generalized to QCD and other QCD-like theories.Comment: 29 pages, expanded discussion of multiple compactified dimension
Finite N Matrix Models of Noncommutative Gauge Theory
We describe a unitary matrix model which is constructed from discrete analogs
of the usual projective modules over the noncommutative torus and use it to
construct a lattice version of noncommutative gauge theory. The model is a
discretization of the noncommutative gauge theories that arise from toroidal
compactification of Matrix theory and it includes a recent proposal for a
non-perturbative definition of noncommutative Yang-Mills theory in terms of
twisted reduced models. The model is interpreted as a manifestly star-gauge
invariant lattice formulation of noncommutative gauge theory, which reduces to
ordinary Wilson lattice gauge theory for particular choices of parameters. It
possesses a continuum limit which maintains both finite spacetime volume and
finite noncommutativity scale. We show how the matrix model may be used for
studying the properties of noncommutative gauge theory.Comment: 17 pp, Latex2e; Typos corrected, references adde
Wilson Loops and QCD/String Scattering Amplitudes
We generalize modern ideas about the duality between Wilson loops and
scattering amplitudes in SYM to large QCD by deriving a
general relation between QCD meson scattering amplitudes and Wilson loops. We
then investigate properties of the open-string disk amplitude integrated over
reparametrizations. When the Wilson loop is approximated by the area behavior,
we find that the QCD scattering amplitude is a convolution of the standard
Koba-Nielsen integrand and a kernel. As usual poles originate from the first
factor, whereas no (momentum dependent) poles can arise from the kernel. We
show that the kernel becomes a constant when the number of external particles
becomes large. The usual Veneziano amplitude then emerges in the kinematical
regime where the Wilson loop can be reliably approximated by the area behavior.
In this case we obtain a direct duality between Wilson loops and scattering
amplitudes when spatial variables and momenta are interchanged, in analogy with
the =4 SYM case.Comment: 39pp., Latex, no figures; v2: typos corrected; v3: final, to appear
in PR
Light baryon masses in different large- limits
We investigate the behavior of light baryon masses in three inequivalent
large- limits: 't~Hooft, QCD and Corrigan-Ramond. Our
framework is a constituent quark model with relativistic-type kinetic energy,
stringlike confinement and one-gluon-exchange term, thus leading to
well-defined results even for massless quarks. We analytically prove that the
light baryon masses scale as , and in the 't~Hooft, QCD and Corrigan-Ramond limits respectively. Those results confirm previous
ones obtained by using either diagrammatic methods or constituent approaches,
mostly valid for heavy quarks.Comment: Final version to appear in Phys. Rev.
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