481 research outputs found
SU(N) gauge theories in 2+1 dimensions -- further results
We calculate the string tension and part of the mass spectrum of SU(4) and
SU(6) gauge theories in 2+1 dimensions using lattice techniques. We combine
these new results with older results for N=2,...,5 so as to obtain more
accurate extrapolations to N=infinity. The qualitative conclusions of the
earlier work are unchanged: SU(N) theories in 2+1 dimensions are linearly
confining as N->infinity; the limit is achieved by keeping g.g.N fixed; SU(3),
and even SU(2), are `close' to SU(infinity). We obtain more convincing evidence
than before that the leading large-N correction is O(1/N.N). We look for the
multiplication of states that one expects in simple flux loop models of
glueballs, but find no evidence for this.Comment: 15 page
SU(N) gauge theories in four dimensions: exploring the approach to N = infinity
We calculate the string tension, K, and some of the lightest glueball masses,
M, in 3+1 dimensional SU(N) lattice gauge theories for N=2,3,4,5 . From the
continuum extrapolation of the lattice values, we find that the mass ratios,
M/sqrt(K), appear to show a rapid approach to the large-N limit, and, indeed,
can be described all the way down to SU(2) using just a leading O(1/NxN)
correction. We confirm that the smooth large-N limit we find, is obtained by
keeping a constant 't Hooft coupling. We also calculate the topological charge
of the gauge fields. We observe that, as expected, the density of small-size
instantons vanishes rapidly as N increases, while the topological
susceptibility appears to have a non-zero N=infinity limit.Comment: Discussion on the correlation time of the topological charge improved
and 1 figure added; other minor changes; conclusions unchanged. To appear on
JHE
Glueball masses in the large N limit
The lowest-lying glueball masses are computed in SU() gauge theory on a
spacetime lattice for constant value of the lattice spacing and for
ranging from 3 to 8. The lattice spacing is fixed using the deconfinement
temperature at temporal extension of the lattice . The calculation is
conducted employing in each channel a variational ansatz performed on a large
basis of operators that includes also torelon and (for the lightest states)
scattering trial functions. This basis is constructed using an automatic
algorithm that allows us to build operators of any size and shape in any
irreducible representation of the cubic group. A good signal is extracted for
the ground state and the first excitation in several symmetry channels. It is
shown that all the observed states are well described by their large
values, with modest corrections. In addition spurious states
are identified that couple to torelon and scattering operators. As a byproduct
of our calculation, the critical couplings for the deconfinement phase
transition for N=5 and N=7 and temporal extension of the lattice are
determined.Comment: 1+36 pages, 22 tables, 21 figures. Typos corrected, conclusions
unchanged, matches the published versio
What we do understand of Colour Confinement
A review is presented of what we understand of colour confinement in QCD.
Lattice formulation provides evidence that QCD vacuum is a dual superconductor:
the chromoelectric field of a pair is constrained by dual Meissner
effect into a dual Abrikosov flux tube and the static potential energy is
proportional to the distance.Comment: 10 pages, 5 figures, plenary talk at "Quark Matter 99", Torino,
Italy, May 10-15, 199
Is Confinement a Phase of Broken Dual Gauge Symmetry?
We study whether broken dual gauge symmetry, as detected by a monopole order
parameter introduced by the Pisa group, is necessarily associated with the
confinement phase of a lattice gauge theory. We find a number of examples,
including SU(2) gauge-Higgs theory, mixed fundamental-adjoint SU(2) gauge
theory, and pure SU(5) gauge theory, which appear to indicate a dual gauge
symmetry transition in the absence of a transition to or from a confined phase.
While these results are not necessarily fatal to the dual superconductor
hypothesis, they may pose some problems of interpretation for the present
formulation of the Pisa monopole criterion.Comment: 6 pages, 5 figure
k-String tensions and their large-N dependence
We consider whether the 1/N corrections to k-string tensions must begin at
order 1/N^2, as in the Sine Law, or whether odd powers of 1/N, as in Casimir
Scaling, are also acceptable. The issue is important because different models
of confinement differ in their predictions for the representation-dependence of
k-string tensions, and corrections involving odd powers of 1/N would seem to be
ruled out by the large-N expansion. We show, however, that k-string tensions
may, in fact, have leading 1/N corrections, and consistency with the large-N
expansion, in the open string sector, is achieved by an exact pairwise
cancellation among terms involving odd powers of 1/N in particular combinations
of Wilson loops. It is shown how these cancellations come about in a concrete
example, namely, strong coupling lattice gauge theory with the heat-kernel
action, in which k-string tensions follow the Casimir scaling rule.Comment: Talk presented at the XXIX International Symposium on Lattice Field
Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi
The deconfining phase transition in SU(N) gauge theories
We report on our ongoing investigation of the deconfining phase transition in
SU(4) and SU(6) gauge theories. We calculate the critical couplings while
taking care to avoid the influence of a nearby bulk phase transition. We
determine the latent heat of the phase transition and investigate the order and
the strength of the transition at large N. We also report on our determination
of the critical temperature expressed in units of the string tension in the
large N limit.Comment: Lattice 2002 (nonzerot), 3 pages, 2 figure
Features of SU(N) Gauge Theories
We review recent lattice results for the large limit of SU(N) gauge
theories. In particular, we focus on glueball masses, topology and its relation
to chiral symmetry breaking (relevant for phenomenology), on the tension of
strings connecting sources in higher representations of the gauge group
(relevant for models of confinement and as a comparative ground for theories
beyond the Standard Model) and on the finite temperature deconfinement phase
transition (relevant for RHIC-like experiments). In the final part we present
open challenges for the future.Comment: 6 pages, 3 figures; summary of the talk given by B. Lucini and the
poster presented by U. Wenger at the conference "Confinement 2003
Topology and Confinement in SU(N) Gauge Theories
The large N limit of SU(N) gauge theories in 3+1 dimensions is investigated
on the lattice by extrapolating results obtained for . A
numerical determination of the masses of the lowest-lying glueball states and
of the topological susceptibility in the limit is provided. Ratios
of the tensions of stable k-strings over the tension of the fundamental string
are investigated in various regimes and the results are compared with
expectations based on several scenarios -- in particular MQCD and Casimir
scaling. While not conclusive at zero temperature in D=3+1, in the other cases
investigated our data seem to favour the latter.Comment: 3 pages, 2 figures; talk presented by B. Lucini at
Lattice2001(confinement
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