253 research outputs found

### Volume dependence in 2+1 Yang-Mills theory

We present the results of an analysis of a 2+1 dimensional pure SU(N)
Yang-Mills theory formulated on a 2-dimensional spatial torus with non-trivial
magnetic flux. We focus on investigating the dependence of the electric-flux
spectrum, extracted from Polyakov loop correlators, with the spatial size l,
the number of colours N, and the magnetic flux m. The size of the torus acts a
parameter that allows to control the onset of non-perturbative effects. In the
small volume regime, where perturbation theory holds, we derive the one-loop
self-energy correction to the single-gluon spectrum, for arbitrary N and m. We
discuss the transition from small to large volumes that has been investigated
by means of Monte-Carlo simulations. We argue that the energy of electric flux
e, for the lowest gluon momentum, depends solely on e/N and on the
dimensionless variable x=lambda N l, with lambda the 't Hooft coupling. The
variable x can be interpreted as the dimensionless 't Hooft coupling for an
effective box size given by Nl. This implies a version of reduction that allows
to trade l by N without modifying the electric-flux energy.Comment: 7 pages, 3 figures. Proceedings of the 30th International Symposium
on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia. Minor change:
Fig. 1 modified to correctly account for the sign convention in Eq. (2.5

### Topological Properties of the QCD Vacuum at T=0 and T ~ T_c

We study on the lattice the topology of SU(2) and SU(3) Yang-Mills theories
at zero temperature and of QCD at temperatures around the phase transition. To
smooth out dislocations and the UV noise we cool the configurations with an
action which has scale invariant instanton solutions for instanton size above
about 2.3 lattice spacings. The corresponding "improved" topological charge
stabilizes at an integer value after few cooling sweeps. At zero temperature
the susceptibility calculated from this charge (about (195MeV)^4 for SU(2) and
(185 MeV)^4 for SU(3)) agrees very well with the phenomenological expectation.
At the minimal amount of cooling necessary to resolve the structure in terms of
instantons and anti-instantons we observe a dense ensemble where the total
number of peaks is by a factor 5-10 larger than the net charge. The average
size observed for these peaks at zero temperature is about 0.4-0.45 fm for
SU(2) and 0.5-0.6 fm for SU(3). The size distribution changes very little with
further cooling, although in this process up to 90% of the peaks disappear by
pair annihilation. For QCD we observe below T_c a reduction of the topological
susceptibility as an effect of the dynamical fermions. Nevertheless also here
the instantons form a dense ensemble with general characteristics similar to
those of the quenched theory. A further drop in the susceptibility above T_c is
also in rough agreement with what has been observed for pure SU(3). We see no
clear signal for dominant formation of instanton - anti-instanton molecules.Comment: Latex, 7 pages, 4 figures (one colour). Contribution to the 31st
International Symposium Ahrenshoop on the Theory of Elementary Particles,
Buckow, September 2-6, 199

### Primordial magnetic fields from preheating at the electroweak scale

We analyze the generation of helical magnetic fields during preheating in a
model of low-scale electroweak (EW) hybrid inflation. We show how the
inhomogeneities in the Higgs field, resulting from tachyonic preheating after
inflation, seed the magnetic fields in a way analogous to that predicted by
Vachaspati and Cornwall in the context of the EW symmetry breaking. At this
stage, the helical nature of the generated magnetic fields is linked to the
non-trivial winding of the Higgs-field. We analyze non-perturbatively the
evolution of these helical seeds through the highly non-linear stages of
symmetry breaking (SB) and beyond. Electroweak SB occurs via the nucleation and
growth of Higgs bubbles which squeeze the magnetic fields into string-like
structures. The W-boson charge density clusters in lumps around the magnetic
strings. After symmetry breaking, a detailed analysis of the magnetic field
Fourier spectrum shows two well differentiated components: a UV radiation tail
at a temperature T ~ 0.23 m_higgs slowly growing with time, and an IR peak
associated to the helical magnetic fields, which seems to follow inverse
cascade. The system enters a regime in which we observe that both the amplitude
(\rho_B/\rho_{EW} ~ 0.01) and the correlation length of the magnetic field grow
linearly with time. During this stage of evolution we also observe a power-law
growth in the helical susceptibility. These properties support the possibility
that our scenario could provide the seeds eventually evolving into the
microgauss fields observed today in galaxies and clusters of galaxies.Comment: 55 pages, late

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