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, 1992–98

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)