816 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

### 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

### 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

### 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

### 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

### 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

### Ghost decoupling in 't Hooft spectrum for mesons

We show that the replacement of the ``instantaneous'' 't Hooft's potential
with the causal form suggested by equal time canonical quantization in
light-cone gauge, which entails the occurrence of negative probability states,
does not change the bound state spectrum when the difference is treated as a
single insertion in the kernel.Comment: 7 pages, revtex, no figure

### Anomalous dimensions and ghost decoupling in a perturbative approach to the generalized chiral Schwinger model

A generalized chiral Schwinger model is studied by means of perturbative
techniques. Explicit expressions are obtained, both for bosonic and fermionic
propagators, and compared to the ones derived by means of functional
techniques. In particular a consistent recipe is proposed to describe the
ambiguity occurring in the regularization of the fermionic determinant. The
role of the gauge fixing term, which is needed to develop perturbation theory
and the behaviour of the spectrum as a function of the parameters are clarified
together with ultraviolet and infrared properties of the model.Comment: DFPD 94/TH/29, May 1994, 28 pages, Late

### Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription

The exact Wilson loop expression for the pure Yang-Mills U(N) theory on a
sphere $S^2$ of radius $R$ exhibits, in the decompactification limit $R\to
\infty$, the expected pure area exponentiation. This behaviour can be
understood as due to the sum over all instanton sectors. If only the zero
instanton sector is considered, in the decompactification limit one exactly
recovers the sum of the perturbative series in which the light-cone gauge
Yang-Mills propagator is prescribed according to Wu-Mandelstam-Leibbrandt. When
instantons are disregarded, no pure area exponentiation occurs, the string
tension is different and, in the large-N limit, confinement is lost.Comment: RevTex, 11 pages, two references adde

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