26 research outputs found
Edge Singularity in ``Induced QCD"
The behaviour of the master field in ``induced QCD" near the edge of its
support is studied. An extended scaling domain, where the shape of the master
field is a universal function, is found. This function is determined explicitly
for the case of dimensions, close to one, and the -expansion is
constructed. The problem of the meson spectrum corresponding to this solution
is analyzed. As a byproduct of these calculations, a new, explicit equation for
the meson spectrum in ``induced QCD" with a general potential is derived.Comment: 23 pages, preprint PUPT-146
On the Large N Limit of the Itzykson-Zuber Integral
We study the large N limit of the Itzykson -- Zuber integral and show that
the leading term is given by the exponent of an action functional for the
complex inviscid Burgers (Hopf) equation evaluated on its particular classical
solution; the eigenvalue densities that enter in the IZ integral being the
imaginary parts of the boundary values of this solution. We show how this
result can be applied to ``induced QCD" with an arbitrary potential . We
find that for a nonsingular in one dimension the eigenvalue density
at the saddle point is the solution of the functional equation
, where . As an illustration we present a
number of new particular solutions of the matrix model on a discrete real
line.Comment: 19 page
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
Adding and multiplying random matrices: a generalization of Voiculescu's formulae
In this paper, we give an elementary proof of the additivity of the
functional inverses of the resolvents of large random matrices, using
recently developed matrix model techniques. This proof also gives a very
natural generalization of these formulae to the case of measures with an
external field. A similar approach yields a relation of the same type for
multiplication of random matrices.Comment: 11 pages, harvmac. revised x 2: refs and minor comments adde
A new large N phase transition in YM2
Inspired by the interpretation of two dimensional Yang-Mills theory on a
cylinder as a random walk on the gauge group, we point out the existence of a
large N transition which is the gauge theory analogue of the cutoff transition
in random walks. The transition occurs in the strong coupling region, with the
't Hooft coupling scaling as alpha*log(N), at a critical value of alpha (alpha
= 4 on the sphere). The two phases below and above the transition are studied
in detail. The effective number of degrees of freedom and the free energy are
found to be proportional to N^(2-alpha/2) below the transition and to vanish
altogether above it. The expectation value of a Wilson loop is calculated to
the leading order and found to coincide in both phases with the strong coupling
value.Comment: 23 pages, 3 figure
Modulation theory of quantum tunneling into a Calogero-Sutherland fluid
Quantum hydrodynamics of interacting electrons with a parabolic single
particle spectrum is studied using the Calogero-Sutherland model. The effective
action and modulation equations, describing evolution of periodic excitations
in the fluid, are derived. Applications to the problem of a single electron
tunneling into the FQHE edge state are discussed
Deconfinement Transition in Large N Lattice Gauge Theory
We study analytically the phase diagram of the pure lattice gauge
theory at finite temperature, and we attempt to estimate the critical
deconfinement temperature. We apply large techniques to the Wilson and to
the Heat Kernel action, and we study the resulting models both in the strong
coupling and in the weak coupling limits. Using the Heat Kernel action, we
establish an interesting connection between the Douglas-Kazakov phase
transition of two-dimensional QCD and the deconfining transition in
dimensions. The analytic results obtained for the critical temperature compare
well with Montecarlo simulations of the full theory in and in
dimensions.Comment: 39 pages (Latex) + 4 ps-figures (using EPSF), DFTT 30/9
Distributional impact of taxes and social transfers in Russia over the downturn
Low oil prices and the recession in Russia which started in 2014 are increasing pressures for fiscal consolidation, after more than a decade of prosperity. This paper assesses the distributional impact of the main tax and social spending programs in Russia in 2014 by applying a state-of-the-art incidence analysis. Overall, the Russian welfare state achieves a moderate reduction in inequality through tax-benefit policies by international standards. Most redistribution occurs through pensions. Major limits on the redistributive effect of tax-benefit policy include the large share of tax revenues that come from (regressive) indirect taxes, the neutral impact of personal income taxes and the low share of spending that goes on social assistance targeted to low-income groups. Tax-benefit policy also has an important impact on the age distribution of income, as households of working-age people (with and without children) subsidize pensioner households