2,191 research outputs found

### Two-dimensional Yang-Mills theory: perturbative and instanton contributions, and its relation to QCD in higher dimensions

Two different scenarios (light-front and equal-time) are possible for
Yang-Mills theories in two dimensions. The exact $\bar q q$-potential can be
derived in perturbation theory starting from the light-front vacuum, but
requires essential instanton contributions in the equal-time formulation. In
higher dimensions no exact result is available and, paradoxically, only the
latter formulation (equal-time) is acceptable, at least in a perturbative
context.Comment: latex 10 pages, no figures. Plenary session talk at the Meeting
``Constrained dynamics and quantum gravity 99'', Villasimius (Sardinia-Italy)
September 13-17, 1999; minor change

### The Pole Part of the 1PI Four-Point Function in Light-Cone Gauge Yang-Mills Theory

The complete UV-divergent contribution to the one-loop 1PI four-point
function of Yang-Mills theory in the light-cone gauge is computed in this
paper. The formidable UV-divergent contributions arising from each four-point
Feynman diagram yield a succinct final result which contains nonlocal terms as
expected. These nonlocal contributions are consistent with gauge symmetry, and
correspond to a nonlocal renormalization of the wave function. Renormalization
of Yang-Mills theory in the light-cone gauge is thus shown explicitly at the
one-loop level.Comment: 35 pages, 18 figures. To be published in Nuc. Phys.

### Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge

Complete two-loop calculation of a dimensionally regularized Wilson loop with
light-like segments is performed in the light-like axial gauge with the
Mandelstam-Leibbrandt prescription for the gluon propagator. We find an
expression which {\it exactly} coincides with the one previously obtained for
the same Wilson loop in covariant Feynman gauge. The renormalization of Wilson
loop is performed in the \MS-scheme using a general procedure tailored to the
light-like axial gauge. We find that the renormalized Wilson loop obeys a
renormalization group equation with the same anomalous dimensions as in
covariant gauges. Physical implications of our result for investigation of
infrared asymptotics of perturbative QCD are pointed out.Comment: 24 pages and 4 figures (included), LaTeX style, UFPD-93/TH/23,
UPRF-93-366, UTF-93-29

### Two-dimensional Yang-Mills theory in the leading 1/N expansion revisited

We obtain a formal solution of an integral equation for $q\bar q$ bound
states, depending on a parameter \eta which interpolates between 't Hooft's
(\eta=0) and Wu's (\eta=1) equations. We also get an explicit approximate
expression for its spectrum for a particular value of the ratio of the coupling
constant to the quark mass. The spectrum turns out to be in qualitative
agreement with 't Hooft's as long as \eta \neq 1. In the limit \eta=1 (Wu's
case) the entire spectrum collapses to zero, in particular no rising Regge
trajectories are found.Comment: CERN-TH/96-364, 13 pages, revTeX, no figure

### Infrared singularities in the null-plane bound-state equation when going to 1+1 dimensions

In this paper we first consider the null-plane bound-state equation for a $q
\bar q$ pair in 1+3 dimensions and in the lowest-order Tamm-Dancoff
approximation. Light-cone gauge is chosen with a causal prescription for the
gauge pole in the propagator. Then we show that this equation, when
dimensionally reduced to 1+1 dimensions, becomes 't Hooft's bound-state
equation, which is characterized by an $x^+$-instantaneous interaction. The
deep reasons for this coincidence are carefully discussed.Comment: 18 pages, revTeX, no figure

### Wilson loops in the adjoint representation and multiple vacua in two-dimensional Yang-Mills theory

$QCD_2$ with fermions in the adjoint representation is invariant under
$SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure
(k-sectors). The static potential between adjoint charges, in the limit of
infinite mass, can be therefore obtained by computing Wilson loops in the pure
Yang-Mills theory with the same non-trivial structure. When the (Euclidean)
space-time is compactified on a sphere $S^2$, Wilson loops can be exactly
expressed in terms of an infinite series of topological excitations
(instantons). The presence of k-sectors modifies the energy spectrum of the
theory and its instanton content. For the exact solution, in the limit in which
the sphere is decompactified, a k-sector can be mimicked by the presence of
k-fundamental charges at $\infty$, according to a Witten's suggestion. However
this property neither holds before decompactification nor for the genuine
perturbative solution which corresponds to the zero-instanton contribution on
$S^2$.Comment: RevTeX, 46 pages, 1 eps-figur

### Renormalization in light--cone gauge: how to do it in a consistent way

We summarize several basic features concerning canonical equal time
quantization and renormalization of Yang--Mills theories in light--cone gauge.
We describe a ``two component" formulation which is reminiscent of the
light--cone hamiltonian perturbation rules. Finally we review the derivation of
the one--loop Altarelli--Parisi densities, using the correct causal
prescription on the ``spurious" pole.Comment: Invited report at the Workshop ``QCD and QED in Higher Order",
Rheinsberg, April 1996. 17 pages, revtex, no figure

### Fiscal policy and price stability: the case of Italy, 1992â98

Many authorities at home and abroad questioned Italy's ability to meet the strict criteria to join the European Monetary Union. The author looks at the interaction between fiscal policy and monetary policy in Italy between 1992, when it exited the European Exchange Rate Mechanism, and 1998, when an official announcement was made that it would join the union.Fiscal policy ; Monetary policy ; Price regulation

### Equilibrium and government commitment

How should a government use the power to commit to ensure a desirable equilibrium outcome? In this paper, I show a misleading aspect of what has become a standard approach to this question, and I propose an alternative. I show that the complete description of an optimal (indeed, of any) policy scheme requires outlining the consequences of paths that are often neglected. The specification of policy along those paths is crucial in determining which schemes implement a unique equilibrium and which ones leave room for multiple equilibria that depend on the expectations of the private sector.Equilibrium (Economics)

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