1,017 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
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
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
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
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
Vortices and confinement in hot and cold D=2+1 gauge theories
We calculate the variation with temperature of the vortex free energy in
D=2+1 SU(2) lattice gauge theories. We do so both above and below the
deconfining transition at T=Tc. We find that this quantity is zero at all T for
large enough volumes. For T<Tc this observation is consistent with the fact
that the phase is linearly confining; while for T>Tc it is consistent with the
conventional expectation of `spatial' linear confinement. In small spatial
volumes this quantity is shown to be non-zero. The way it decreases to zero
with increasing volume is shown to be controlled by the (spatial) string
tension and it has the functional form one would expect if the vortices being
studied were responsible for the confinement at low T, and for the `spatial'
confinement at large T. We also discuss in detail some of the direct numerical
evidence for a non-zero spatial string tension at high T, and we show that the
observed linearity of the (spatial) potential extends over distances that are
large compared to typical high-T length scales.Comment: 27 pages, 6 figure
Z2 monopoles in D=2+1 SU(2) lattice gauge theory
We calculate the Euclidean action of a pair of Z2 monopoles (instantons), as
a function of their spatial separation, in D=2+1 SU(2) lattice gauge theory. We
do so both above and below the deconfining transition at T=Tc. At high T, and
at large separation, we find that the monopole `interaction' grows linearly
with distance: the flux between the monopoles forms a flux tube (exactly like a
finite portion of a Z2 domain wall) so that the monopoles are linearly
confined. At short distances the interaction is well described by a Coulomb
interaction with, at most, a very small screening mass, possibly equal to the
Debye electric screening mass. At low T the interaction can be described by a
simple screened Coulomb (i.e. Yukawa) interaction with a screening mass that
can be interpreted as the mass of a `constituent gluon'. None of this is
unexpected, but it helps to resolve some apparent controversies in the recent
literature.Comment: 14 pages, 2 figure
G_2 gauge theory at finite temperature
The gauge group being centreless, gauge theory is a good laboratory for
studying the role of the centre of the group for colour confinement in
Yang-Mills gauge theories. In this paper, we investigate pure gauge
theory at finite temperature on the lattice. By studying the finite size
scaling of the plaquette, the Polyakov loop and their susceptibilities, we show
that a deconfinement phase transition takes place. The analysis of the
pseudocritical exponents give strong evidence of the deconfinement transition
being first order. Implications of our findings for scenarios of colour
confinement are discussed.Comment: 17 pages, 8 figure
SO(2N) and SU(N) gauge theories in 2+1 dimensions
We perform an exploratory investigation of how rapidly the physics of SO(2N)
gauge theories approaches its N=oo limit. This question has recently become
topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge
theories, but do not have a finite chemical potential sign problem. We consider
only the pure gauge theory and, because of the inconvenient location of the
lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely
confine our numerical calculations to 2+1 dimensions. We discuss analytic
expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do
indeed appear to be the same, and show that a number of mass ratios do indeed
appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge
theories are quite similar except for the values of the string tension and
coupling, both of which differences can be readily understood.Comment: 27 pages, 9 figure
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