505 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

### Chiral symmetry breaking in the 3-d Thirring model for small $N_f$

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 $U(1)$ symmetry
corresponding to monopole charge conservation. This operator is tested by
numerical simulations in compact $U(1)$ 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

### 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

### N-ality and topology at finite temperature

We study the spectrum of confining strings in SU(3) pure gauge theory, in
different representations of the gauge group. Our results provide direct
evidence that the string spectrum agrees with predictions based on n-ality. We
also investigate the large-N behavior of the topological susceptibility $\chi$
in four-dimensional SU(N) gauge theories at finite temperature, and in
particular across the finite-temperature transition at $T_c$. The results
indicate that $\chi$ has a nonvanishing large-N limit for $T<T_c$, 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, $\chi$ shows a large suppression. The comparison between the data
for N=4 and N=6 hints at a vanishing large-N limit for $T>T_c$.Comment: 3 pages, 2 figures. Presented at Lattice2004(topology

### Local coherence and deflation of the low quark modes in lattice QCD

The spontaneous breaking of chiral symmetry in QCD is known to be linked to a
non-zero density of eigenvalues of the massless Dirac operator near the origin.
Numerical studies of two-flavour QCD now suggest that the low quark modes are
locally coherent to a certain extent. As a consequence, the modes can be
simultaneously deflated, using local projectors, with a total computational
effort proportional to the lattice volume (rather than its square). Deflation
has potentially many uses in lattice QCD. The technique is here worked out for
the case of quark propagator calculations, where large speed-up factors and a
flat scaling behaviour with respect to the quark mass are achieved.Comment: Plain TeX, 23 pages, 4 figures included; minor text modifications;
version published in JHE

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