50 research outputs found
Correlators of the Kazakov-Migdal Model
We derive loop equations for the one-link correlators of gauge and scalar
fields in the Kazakov-Migdal model. These equations determine the solution of
the model in the large N limit and are similar to analogous equations for the
Hermitean two-matrix model. We give an explicit solution of the equations for
the case of a Gaussian, quadratic potential. We also show how similar
calculations in a non-Gaussian case reduce to purely algebraic equations.Comment: 14 pages, ITEP-YM-3-9
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.
Breakdown of large-N quenched reduction in SU(N) lattice gauge theories
We study the validity of the large-N equivalence between four-dimensional
SU(N) lattice gauge theory and its momentum quenched version--the Quenched
Eguchi-Kawai (QEK) model. We find that the assumptions needed for the proofs of
equivalence do not automatically follow from the quenching prescription. We use
weak-coupling arguments to show that large-N equivalence is in fact likely to
break down in the QEK model, and that this is due to dynamically generated
correlations between different Euclidean components of the gauge fields. We
then use Monte-Carlo simulations at intermediate couplings with 20 <= N <= 200
to provide strong evidence for the presence of these correlations and for the
consequent breakdown of reduction. This evidence includes a large discrepancy
between the transition coupling of the "bulk" transition in lattice gauge
theories and the coupling at which the QEK model goes through a strongly
first-order transition. To accurately measure this discrepancy we adapt the
recently introduced Wang-Landau algorithm to gauge theories.Comment: 51 pages, 16 figures, Published verion. Historical inaccuracies in
the review of the quenched Eguchi-Kawai model are corrected, discussion on
reduction at strong-coupling added, references updated, typos corrected. No
changes to results or conclusion
Generalized Penner models to all genera
We give a complete description of the genus expansion of the one-cut solution
to the generalized Penner model. The solution is presented in a form which
allows us in a very straightforward manner to localize critical points and to
investigate the scaling behaviour of the model in the vicinity of these points.
We carry out an analysis of the critical behaviour to all genera addressing all
types of multi-critical points. In certain regions of the coupling constant
space the model must be defined via analytical continuation. We show in detail
how this works for the Penner model. Using analytical continuation it is
possible to reach the fermionic 1-matrix model. We show that the critical
points of the fermionic 1-matrix model can be indexed by an integer, , as it
was the case for the ordinary hermitian 1-matrix model. Furthermore the 'th
multi-critical fermionic model has to all genera the same value of
as the 'th multi-critical hermitian model. However, the
coefficients of the topological expansion need not be the same in the two
cases. We show explicitly how it is possible with a fermionic matrix model to
reach a multi-critical point for which the topological expansion has
alternating signs, but otherwise coincides with the usual Painlev\'{e}
expansion.Comment: 27 pages, PostScrip
Worldline Casting of the Stochastic Vacuum Model and Non-Perturbative Properties of QCD: General Formalism and Applications
The Stochastic Vacuum Model for QCD, proposed by Dosch and Simonov, is fused
with a Worldline casting of the underlying theory, i.e. QCD. Important,
non-perturbative features of the model are studied. In particular,
contributions associated with the spin-field interaction are calculated and
both the validity of the loop equations and of the Bianchi identity are
explicitly demonstrated. As an application, a simulated meson-meson scattering
problem is studied in the Regge kinematical regime. The process is modeled in
terms of the "helicoidal" Wilson contour along the lines introduced by Janik
and Peschanski in a related study based on a AdS/CFT-type approach. Working
strictly in the framework of the Stochastic Vacuum Model and in a semiclassical
approximation scheme the Regge behavior for the Scattering amplitude is
demonstrated. Going beyond this approximation, the contribution resulting from
boundary fluctuation of the Wilson loop contour is also estimated.Comment: 37 pages, 1 figure. Final version to appear in Phys.Rev.
A Brief Introduction to Wilson Loops and Large N
A pedagogical introduction to Wilson loops, lattice gauge theory and the
1/N-expansion of QCD is presented. The three introductory lectures were given
at the 37th ITEP Winter School of Physics, Moscow, February 9-16, 2009.Comment: 14 pages, 14 figures, Lectures at the 37th ITEP Winter School of
Physic
Spin contribution to light baryons in different large- limits
We investigate the spin contribution to light baryon ground states in three
inequivalent large- limits: 't Hooft, QCD antisymmetric and QCD symmetric.
Our framework is a constituent quark model with a relativistic Hamiltonian
containing a stringlike confinement and a one-gluon exchange term. Two
spin-dependent potentials are considered and treated as perturbations: the
color magnetic interaction stemming from the one-gluon exchange process and the
chiral boson exchange interaction. We analytically prove that the spin
contributions scale like , where is the total spin and is
the number of quark, in agreement with diagrammatic methods. Both potentials
yield also -independent contributions which scale at most as O.Comment: 1 figur
Multiloop correlators for two-dimensional quantum gravity
We find explicitly all multi-loop correlators in the complex matrix model to the leading order in 1/N and show that they are identical to the even part of the multi-loop correlators in the hermitean matrix model. The scaling limit for the corresponding macroscopic loop correlators is constructed and agrees with the one of the hermitean model to all orders in 1/N 2. In particular the double scaling limits of the two models will lead to identical "string equations"
Anomalous dimensions of leading twist conformal operators
We extend and develop a method for perturbative calculations of anomalous
dimensions and mixing matrices of leading twist conformal primary operators in
conformal field theories. Such operators lie on the unitarity bound and hence
are conserved (irreducible) in the free theory. The technique relies on the
known pattern of breaking of the irreducibility conditions in the interacting
theory. We relate the divergence of the conformal operators via the field
equations to their descendants involving an extra field and accompanied by an
extra power of the coupling constant. The ratio of the two-point functions of
descendants and of their primaries determines the anomalous dimension, allowing
us to gain an order of perturbation theory. We demonstrate the efficiency of
the formalism on the lowest-order analysis of anomalous dimensions and mixing
matrices which is required for two-loop calculations of the former. We compare
these results to another method based on anomalous conformal Ward identities
and constraints from the conformal algebra. It also permits to gain a
perturbative order in computations of mixing matrices. We show the complete
equivalence of both approaches.Comment: 21 pages, 4 figures; references adde
M-Theory of Matrix Models
Small M-theories unify various models of a given family in the same way as
the M-theory unifies a variety of superstring models. We consider this idea in
application to the family of eigenvalue matrix models: their M-theory unifies
various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition
functions) with Kontsevich tau-function. Moreover, the corresponding duality
relations look like direct analogues of instanton and meron decompositions,
familiar from Yang-Mills theory.Comment: 12 pages, contribution to the Proceedings of the Workshop "Classical
and Quantum Integrable Systems", Protvino, Russia, January, 200