654 research outputs found
Topological susceptibility of SU(N) gauge theories at finite temperature
We investigate the large-N behavior of the topological susceptibility in
four-dimensional SU(N) gauge theories at finite temperature, and in particular
across the finite-temperature transition at Tc. For this purpose, we consider
the lattice formulation of the SU(N) gauge theories and perform Monte Carlo
simulations for N=4,6. The results indicate that the topological susceptibility
has a nonvanishing large-N limit for T<Tc, as at T=0, and that the topological
properties remain substantially unchanged in the low-temperature phase. On the
other hand, above the deconfinement phase transition, the topological
susceptibility shows a large suppression. The comparison between the data for
N=4 and N=6 hints at a vanishing large-N limit for T>Tc.Comment: 9 pages, 2 figs, a few discussions added, JHEP in pres
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
Colour confinement and dual superconductivity of the vacuum - I
We study dual superconductivity of the ground state of SU(2) gauge theory, in
connection with confinement. We do that measuring on the lattice a disorder
parameter describing condensation of monopoles. Confinement appears as a
transition to dual superconductor, independent of the abelian projection
defining monopoles. Some speculations are made on the existence of a more
appropriate disorder parameter. A similar study for SU(3) is presented in a
companion paper.Comment: Some typos corrected, acknowledgements added; to appear on Phys. Rev.
Free energy and theta dependence of SU(N) gauge theories
We study the dependence of the free energy on the CP violating angle theta,
in four-dimensional SU(N) gauge theories with N >= 3, and in the large-N limit.
Using the Wilson lattice formulation for numerical simulations, we compute
the first few terms of the expansion of the ground-state energy F(theta) around
theta = 0, F(theta) - F(0) = A_2 theta^2 (1 + b_2 theta^2 + ...). Our results
support Witten's conjecture: F(theta) - F(0) = A theta^2 + O(1/N) for theta <
pi.
We verify that the topological susceptibility has a nonzero large-N limit
chi_infinity = 2A with corrections of O(1/N^2), in substantial agreement with
the Witten-Veneziano formula which relates chi_infinity to the eta' mass.
Furthermore, higher order terms in theta are suppressed; in particular, the
O(theta^4) term b_2 (related to the eta' - eta' elastic scattering amplitude)
turns out to be quite small: b_2 = -0.023(7) for N=3, and its absolute value
decreases with increasing N, consistently with the expectation b_2 = O(1/N^2).Comment: 3 pages, talk presented at the conference Lattice2002(topology). v2:
One reference has been updated, no further change
Conformal vs confining scenario in SU(2) with adjoint fermions
The masses of the lowest-lying states in the meson and in the gluonic sector
of an SU(2) gauge theory with two Dirac flavors in the adjoint representation
are measured on the lattice at a fixed value of the lattice coupling for values of the bare fermion mass that span a range
between the quenched regime and the massless limit, and for various lattice
volumes. Even for light constituent fermions the lightest glueballs are found
to be lighter than the lightest mesons. Moreover, the string tension between
two static fundamental sources strongly depends on the mass of the dynamical
fermions and becomes of the order of the inverse squared lattice linear size
before the chiral limit is reached. The implications of these findings for the
phase of the theory in the massless limit are discussed and a strategy for
discriminating between the (near--)conformal and the confining scenario is
outlined.Comment: 5 pages, 4 figures using RevTeX4, Typos corrected, references added.
Versions to appear on PR
Casimir scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theories
We perform lattice calculations of the spatial 't Hooft k-string tensions in
the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to
a factor of T) the surface tensions of the domain walls between the
corresponding (Euclidean) deconfined phases. For T much larger than Tc our
results match on to the known perturbative result, which exhibits Casimir
Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger
and, not surprisingly, our calculations show large deviations from the
perturbative T-dependence. Despite this we find that the behaviour proportional
to k(N-k) persists very accurately down to temperatures very close to Tc. Thus
the Casimir Scaling of the 't Hooft tension appears to be a `universal' feature
that is more general than its appearance in the low order high-T perturbative
calculation. We observe the `wetting' of these k-walls at T around Tc and the
(almost inevitable) `perfect wetting' of the k=N/2 domain wall. Our
calculations show that as T tends to Tc the magnitude of the spatial `t Hooft
string tension decreases rapidly. This suggests the existence of a (would-be)
't Hooft string condensation transition at some temperature which is close to
but below Tc. We speculate on the `dual' relationship between this and the
(would-be) confining string condensation at the Hagedorn temperature that is
close to but above Tc.Comment: 40 pages, 14 figure
Biologia de ninfas de mosca branca Bemisia tabaci BiĂłtipo B (Hemiptera: Aleyrodidae) em cultivares de soja.
Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators
We test a variety of blocking and smearing algorithms for constructing
glueball and string wave-functionals, and find some with much improved overlaps
onto the lightest states. We use these algorithms to obtain improved results on
the tensions of k-strings in SU(4), SU(6), and SU(8) gauge theories. We
emphasise the major systematic errors that still need to be controlled in
calculations of heavier k-strings, and perform calculations in SU(4) on an
anisotropic lattice in a bid to minimise one of these. All these results point
to the k-string tensions lying part-way between the `MQCD' and `Casimir
Scaling' conjectures, with the power in 1/N of the leading correction lying in
[1,2]. We also obtain some evidence for the presence of quasi-stable strings in
calculations that do not use sources, and observe some near-degeneracies
between (excited) strings in different representations. We also calculate the
lightest glueball masses for N=2, ...,8, and extrapolate to N=infinity,
obtaining results compatible with earlier work. We show that the N=infinity
factorisation of the Euclidean correlators that are used in such mass
calculations does not make the masses any less calculable at large N.Comment: 49 pages, 15 figure
Topological susceptibility in the SU(3) gauge theory
We compute the topological susceptibility for the SU(3) Yang--Mills theory by
employing the expression of the topological charge density operator suggested
by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3),
which corresponds to chi=(191 +/- 5 MeV)^4 if F_K is used to set the scale. Our
result supports the Witten--Veneziano explanation for the large mass of the
eta'.Comment: Final version to appear on Phys. Rev. Let
A three-dimensional scalar field theory model of center vortices and its relation to k-string tensions
In d=3 SU(N) gauge theory, we study a scalar field theory model of center
vortices that furnishes an approach to the determination of so-called k-string
tensions. This model is constructed from string-like quantum solitons
introduced previously, and exploits the well-known relation between string
partition functions and scalar field theories in d=3. Center vortices
corresponding to magnetic flux J (in units of 2\pi /N) are composites of J
elementary J=1 constituent vortices that come in N-1 types, with repulsion
between like constituents and attraction between unlike constituents. The
scalar field theory involves N scalar fields \phi_i (one of which is
eliminated) that can merge, dissociate, and recombine while conserving flux mod
N. The properties of these fields are deduced directly from the corresponding
gauge-theory quantum solitons. Every vacuum Feynman graph of the theory
corresponds to a real-space configuration of center vortices. We study
qualitatively the problem of k-string tensions at large N, whose solution is
far from obvious in center-vortex language. We construct a simplified dynamical
picture of constituent-vortex merging, dissociation, and recombination, which
allows in principle for the determination of vortex areal densities and
k-string tensions. This picture involves point-like "molecules" (cross-sections
of center vortices) made of constituent "atoms" that combine and disassociate
dynamically in a d=2 test plane . The vortices evolve in a Euclidean "time"
which is the location of the test plane along an axis perpendicular to the
plane. A simple approximation to the molecular dynamics is compatible with
k-string tensions that are linear in k for k<< N, as naively expected.Comment: 21 pages; RevTeX4; 4 .eps figure
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