1+1 Dimensional Yang-Mills Theories in Light-Cone Gauge

In 1+1 dimensions two different formulations exist of SU(N) Yang Mills theories in light-cone gauge; only one of them gives results which comply with the ones obtained in Feynman gauge. Moreover the theory, when considered in 1+(D-1) dimensions, looks discontinuous in the limit D=2. All those features are proven in Wilson loop calculations as well as in the study of the $q\bar q$ bound state integral equation in the large N limit.Comment: Invited report at the Workshop "Low Dimensional Field Theory", Telluride (CO), Aug. 5-17 1996; 16 pages, latex, no figures To appear in International Journal of Modern Physics A minor misprints correcte

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

The Mandelstam-Leibbrandt Prescription in Light-Cone Quantized Gauge Theories

Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.Comment: Revtex, 14 pages. One postscript figure (requires psfig). A brief discussion of necessary restrictions on the light-cone current operators has been added, and two references. Final version to appear in Z. Phys.

Time exponentiation of a Wilson loop for Yang-Mills theories in 2+\epsilon dimensions

A rectangular Wilson loop centered at the origin, with sides parallel to space and time directions and length $2L$ and $2T$ respectively, is perturbatively evaluated ${\cal O}(g^4)$ in Feynman gauge for Yang--Mills theory in $1+(D-1)$ dimensions. When $D>2$, there is a dependence on the dimensionless ratio $L/T$, besides the area. In the limit $T \to \infty$, keeping $D>2$, the leading expression of the loop involves only the Casimir constant $C_F$ of the fundamental representation and is thereby in agreement with the expected Abelian-like time exponentiation (ALTE). At $D= 2$ the result depends also on $C_A$, the Casimir constant of the adjoint representation and a pure area law behavior is recovered, but no agreement with ALTE in the limit $T\to\infty$. Consequences of these results concerning two and higher-dimensional gauge theories are pointed out.Comment: RevTex, 28 pages, two figure files include

qqˉq\bar q interaction in light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions

A rectangular Wilson loop with sides parallel to space and time directions is perturbatively evaluated in two light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions, with ``instantaneous'' and ``causal'' interactions between static quarks. In the instantaneous formulation we get Abelian-like exponentiation of the area in terms of $C_F$. In the ``causal'' formulation the loop depends not only on the area, but also on the dimensionless ratio $\beta = {L \over T}$, $2L$ and $2T$ being the lengths of the rectangular sides. Besides it also exhibits dependence on $C_A$. In the limit $T \to \infty$ the area law is recovered, but dependence on $C_A$ survives. Consequences of these results are pointed out.Comment: 30 pages, latex, one figure included as a ps file, an Erratum include

Renormalization of gauge invariant composite operators in light-cone gauge

We generalize to composite operators concepts and techniques which have been successful in proving renormalization of the effective Action in light-cone gauge. Gauge invariant operators can be grouped into classes, closed under renormalization, which is matrix-wise. In spite of the presence of non-local counterterms, an ``effective" dimensional hierarchy still guarantees that any class is endowed with a finite number of elements. The main result we find is that gauge invariant operators under renormalization mix only among themselves, thanks to the very simple structure of Lee-Ward identities in this gauge, contrary to their behaviour in covariant gauges.Comment: 35100 Padova, Italy DFPD 93/TH/53, July 1993 documentstyle[preprint,aps]{revtex

Propagators on the two-dimensional light-cone

Light-cone quantization procedure recently presented is applied to the two-dimensional light-cone theories. By introducing the two distinct null planes it is shown that the modification term in the two-dimensional massless light-cone propagators suggested about twenty years ago vanishs.Comment: LATEX, 9page

Light-Cone Quantization of Gauge Fields

Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the ``discretized'' light-cone quantization of gauge fields are discussed.Comment: SMUHEP/93-20, 17 pages (one figure available separately from the authors). Plain TeX, all macros include