581 research outputs found
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
The phase structure of the 3-d Thirring model
We study the phase structure of the Thirring model in 3-d and find it to be
compatible with the existence of a non gaussian fixed point of RG. A Finite
Size Scaling argument is included in the equation of state in order to avoid
the assumptions usually needed to extrapolate to the thermodynamical limit.Comment: Talk presented at LATTICE96(other models
Chiral symmetry breaking in the 3-d Thirring model for small
We study the dynamical breaking of chiral symmetry in the 3-d Thirring model
for a small number of fermion species. The critical point is identified by
fitting lattice data to an equation of state. The spectrum of the theory is
studied to confirm the phase structure of the model.Comment: 3 pages, 3 figures. Talk presented at Lattice '9
Detecting Dual Superconductivity in the Ground State of Gauge Theory
We explicitly construct a monopole creation operator: its vacuum expectation
value is an order parameter for dual superconductivity, in that, if different
from zero, it signals a spontaneous breaking of the symmetry
corresponding to monopole charge conservation. This operator is tested by
numerical simulations in compact gauge theory. Our construction provides
a general recipe for detection of the condensation of any topological soliton.
In particular our operator can be used to detect dual superconductivity of the
QCD vacuum.Comment: 10 pages, 3 figures avalaible on request. REVTE
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
Vortex solution in 2+1 dimensional Yang-Mills theory at high temperatures
At high temperatures the A_0 component of the Yang--Mills field plays the
role of the Higgs field, and the 1-loop potential V(A_0) plays the role of the
Higgs potential. We find a new stable vortex solution of the
Abrikosov-Nielsen-Olesen type, and discuss its properties and possible
implications.Comment: 8 p., three .eps figures include
The decay of unstable k-strings in SU(N) gauge theories at zero and finite temperature
Sources in higher representations of SU(N) gauge theory at T=0 couple with
apparently stable strings with tensions depending on the specific
representation rather than on its N-ality. Similarly at the deconfining
temperature these sources carry their own representation-dependent critical
exponents. It is pointed out that in some instances one can evaluate exactly
these exponents by fully exploiting the correspondence between the 2+1
dimensional critical gauge theory and the 2d conformal field theory in the same
universality class. The emerging functional form of the Polyakov-line
correlators suggests a similar form for Wilson loops in higher representations
which helps in understanding the behaviour of unstable strings at T=0. A
generalised Wilson loop in which along part of its trajectory a source is
converted in a gauge invariant way into higher representations with same
N-ality could be used as a tool to estimate the decay scale of the unstable
strings.Comment: 18 pages, 4 figures v2: typos correcte
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
The Three Dimensional Thirring Model for N_f=4 and N_f=6
We present Monte Carlo simulation results for the three dimensional Thirring
model for numbers of fermion flavors N_f=4 and 6. For N_f=4 we find a second
order chiral symmetry breaking transition at strong coupling, corresponding to
an ultra-violet fixed point of the renormalisation group defining a non-trivial
continuum limit. The critical exponents extracted from a fit to a model
equation of state are distinct from those found for N_f=2. For N_f=6, in
contrast, we present evidence for tunnelling between chirally symmetric and
broken vacua at strong coupling, implying that the phase transition is first
order and no continuum limit exists. The implications for the phase diagram of
the model in the plane of coupling strength and N_f are briefly discussed.Comment: 29 pages, 13 figure
Confinement and the second vortex of the SU(4) gauge group
We study the potential between static SU(4) sources using the Model of Thick
Center Vortices. Such vortices are characterized by the center elements
and . Fitting the ratios of string tensions to those
obtained in Monte-Carlo calculations of lattice QCD we get , where
is the probability that a vortex of type is piercing a plaquette.
Because of vortices of type two are overlapping vortices of type
one. Therefore, corresponds to the existence of an attractive force
between vortices of type one
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