253 research outputs found

    Volume dependence in 2+1 Yang-Mills theory

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    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

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    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

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    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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