We compute the electrical conductivity of quark-gluon plasma in a strong magnetic field B with quantum field theory at finite temperature using the lowest Landau level approximation. We provide the one-loop result arising from 1-to-2 scattering processes whose kinematics are satisfied by the (1+1) dimensional fermion dispersion relation. Due to the chirality conservation, the conductivity diverges in the massless limit, and is sensitive to the value of the current quark mass. As a result, we find that the conductivity along the direction of the magnetic field is quite large compared with the value at B = 0, mainly because of the small value of the current quark mass. We show that the resummation of the ladder diagrams for the current-current correlator gives rise to only sub-leading contributions beyond the leading-log order, and thus verify our one-loop result at the leading-log accuracy. We also discuss possible implications for the relativistic heavy-ion collisions.

We compute the longitudinal electrical conductivity in the presence of strong background magnetic field in complete leading order of perturbative QCD, based on the assumed hierarchy of scales α s eB (m 2 q , T 2 ) eB. We formulate an effective kinetic theory of lowest Landau level quarks with the leading order QCD collision term arising from 1-to-2 processes that become possible due to 1+1 dimensional Landau level kinematics. In small m q /T 1 regime, the longitudinal conductivity behaves as σ zz ∼ e 2 (eB)T /(α s m 2 q log(T /m q )), where the quark mass dependence can be understood from the chiral anomaly with the axial charge relaxation provided by a finite quark mass m q . We also present parametric estimates for the longitudinal and transverse "color conductivities" in the presence of strong magnetic field, by computing dominant damping rates for quarks and gluons that are responsible for color charge transportation. We observe that the longitudinal color conductivity is enhanced by strong magnetic field, which implies that the sphaleron transition rate in perturbative QCD is suppressed by strong magnetic field due to the enhanced Lenz's law in color field dynamics. *

We investigate the viscosities of the quark-gluon plasma in strong magnetic fields within the leading-log and lowest Landau level (LLL) approximations. We first show that the bulk viscosity in the direction parallel to the magnetic field is the only component that has a contribution from the quarks occupying the LLL. We then compute the bulk viscosity from the Kubo formula and find an intriguing quark-mass dependence as a consequence of a competition between the suppression of the bulk viscosity by conformal symmetry and an enhancement of the mean-free path by chirality conservation, which governs the behavior in the massless limit. The quark contribution to the viscosity along the magnetic field becomes larger than the one in the absence of a magnetic field. We also briefly estimate the other transport coefficients by considering the contribution of gluons. We show that the shear viscosities are suppressed compared to their values in the absence of a magnetic field.

We consider the thermal production of dileptons and photons at temperatures above the critical temperature in QCD. We use a model where color excitations are suppressed by a small value of the Polyakov loop, the semi Quark-Gluon Plasma (QGP). Comparing the semi-QGP to the perturbative QGP, we find a mild enhancement of thermal dileptons. In contrast, to leading logarithmic order in weak coupling there are far fewer hard photons from the semi-QGP than the usual QGP. To illustrate the possible effects on photon and dileptons production in heavy ion collisions, we integrate the rate with a realistic hydrodynamic simulation. Dileptons uniformly exhibit a small flow, but the strong suppression of photons in the semi-QGP tends to bias the elliptical flow of photons to that generated in the hadronic phase.PACS numbers: 11.10. Wx, 12.38.Mh, 25.75.Cj, 25.75.Nq The collisions of heavy nuclei at ultra-relativistic energies can be used to investigate the properties of the Quark-Gluon Plasma (QGP). At both the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), much of the collision takes place at temperatures which are not that far above that for the transition, T c . This is a difficult region to study: perturbative methods can be used at high temperature, but not nearSimilarly, hadronic models are valid at low temperature, but break down near T c [2]. One model of the region above but near T c is the semi-QGP [3][4][5][6]. This incorporates the results of numerical simulations on the lattice [7], which show that colored excitations are strongly suppressed when T → T + c , as the expectation value of the Polyakov loop decreases markedly.A notable property of heavy ion collisions is elliptic flow, how the initial spatial anisotropy of peripheral collisions is transformed into a momentum anisotropy. The large elliptic flow of hadrons can be well modeled by hydrodynamic models in which the QCD medium is close to an ideal fluid [8][9][10].Electromagnetic signals, such as dilepton or photon production, are another valuable probe, since they reflect properties of the quark and gluon distributions of the QGP, and once produced, escape without significant interaction [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For example, if most photons are emitted at high temperature in the QGP, since the flow at early times is small, one would expect a small net elliptic flow for photons. However, recently both the PHENIX experiment at RHIC [22] and the ALICE experiment at the LHC [23] have found a large elliptic flow for photons, comparable to that of hadrons. This is most puzzling [17,18,24].In this paper we present the results for the thermal production of hard dileptons and photons in the semi-QGP, and compare them with those of the perturbative QGP. Surprisingly, we find a sharp qualitative difference between the two. In the semi-QGP, the production of dileptons is similar between the deconfined and confined phases, while photon production is strongly suppressed near T c . We compute to leading ord...