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We study the physical mechanism of how an external magnetic field influences the QCD quark condensate. Two competing mechanisms are identified, both relying on the interaction between the magnetic field and the low quark modes. While the coupling to valence quarks enhances the condensate, the interaction with sea quarks suppresses it in the transition region. The latter `sea effect' acts by ordering the Polyakov loop and, thereby, reduces the number of small Dirac eigenmodes and the condensate. It is most effective around the transition temperature, where the Polyakov loop effective potential is flat and a small correction to it by the magnetic field can have a significant effect. Around the critical temperature, the sea suppression overwhelms the valence enhancement, resulting in a net suppression of the condensate, named inverse magnetic catalysis. We support this physical picture by lattice simulations including continuum extrapolated results on the Polyakov loop as a function of temperature and magnetic field. We argue that taking into account the increase in the Polyakov loop and its interaction with the low-lying modes is essential to obtain the full physical picture, and should be incorporated in effective models for the description of QCD in magnetic fields in the transition region.Comment: 19 pages, 8 figures, new reference added, version accepted for publicatio

We study spin 1/2 isoscalar and isovector candidates in both parity channels for the recently discovered Θ + (1540) pentaquark particle in quenched lattice QCD. Our analysis takes into account all possible uncertainties, such as statistical, finite size and quenching errors when performing the chiral and continuum extrapolations and we have indications that our signal is separated from scattering states. The lowest mass that we find in the I P = 0 − channel is in complete agreement with the experimental value of the Θ + mass. On the other hand, the lowest mass state in the opposite parity I P = 0 + channel is much higher. Our findings suggests that the parity of the Θ + is negative.

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We study the topological content of the vacuum of SU (2) pure gauge theory using lattice simulations. We use a smoothing process based on the renormalization group equation. This removes short distance fluctuations but preserves long distance structure. The action of the smoothed configurations is dominated by instantons, but they still show an area law for Wilson loops with an unchanged string tension. The average radius of an instanton is about 0.2 fm, at a density of about 2 fm −4 .

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.

At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to consist of delocalized modes that are described by random matrix statistics. In the present paper we show that the nature of these eigenmodes changes drastically when the system is driven through the finite temperature cross-over. The lowest Dirac modes that are delocalized at low temperature become localized on the scale of the inverse temperature. At the same time the spectral statistics changes from random matrix to Poisson statistics. We demonstrate this with lattice QCD simulations using 2 + 1 flavors of light dynamical quarks with physical masses. Drawing an analogy with Anderson transitions we also examine the mobility edge separating localized and delocalized modes in the spectrum. We show that it scales in the continuum limit and increases sharply with the temperature.

We study the Anderson-type transition previously found in the spectrum of the QCD quark Dirac operator in the high temperature, quark-gluon plasma phase. Using finite size scaling for the unfolded level spacing distribution, we show that in the thermodynamic limit there is a genuine mobility edge, where the spectral statistics changes from Poisson to Wigner-Dyson statistics in a non-analytic way. We determine the correlation length critical exponent, ν, and find that it is compatible with that of the unitary Anderson model. PACS numbers: 12.38.Gc,72.15Rn,12.38.Mh,11.15.Ha The idea of Anderson localization is more than half a century old [1]. Anderson localization consists in the spatial localization of the states of a system due to quantum interference effects, caused by the presence of disorder. Its simplest realization is provided by the Anderson tightbinding model that aims at describing electronic states in a "dirty" conductor, by mimicking the effect of impurities through a random on-site potential. In three dimensions, as soon as the random potential is switched on, localized states appear at the band edge. However, states remain extended around the band center, beyond a critical energy called the "mobility edge". Increasing the amount of disorder, i.e., increasing the width of the distribution of the random potential, the mobility edge moves towards the band center, and above a certain critical disorder all the states become localized (see Refs. [2,3]).Originally proposed to explain the loss of zero temperature conductance as a result of disorder, localization was later found in a much wider range of physical systems. Anderson transitions have been demonstrated with electromagnetic and sound waves as well as cold atoms (see Ref.[4] and references therein) and recently in strongly interacting matter in its high temperature quark-gluon plasma phase [5]. The last item of the list is rather peculiar since in that case localization occurs on a vastly different length and energy scale from all previously known cases, namely on subnuclear rather than atomic scales.In the microscopic description of strongly interacting matter provided by quantum chromodynamics (QCD), a central role is played by the Dirac operator. Its spectrum encodes important properties of quarks and hadrons. At low temperature, the lowest lying quark eigenmodes of the Dirac operator have long been known to be extended, and the corresponding spectrum to obey WignerDyson statistics as predicted by random matrix theory (RMT) [6]. This has been successfully exploited to study the low-energy properties of QCD [6]. In contrast, in the high-temperature quark-gluon plasma phase no similar description of the low-lying quark modes was available until recently. It was first suggested by García-García and Osborn that the transition from the hadronic to the quark-gluon plasma phase might be an Andersontype transition [7]. Using lattice QCD they qualitatively demonstrated that heating the system through the critical temperature makes the quark states mor...