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We present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on $\mu_B$ , which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-$\mu_B$ plane of the QCD phase diagram., Comment: 4 pages, 5 figures, Proceedings of Quark Matter 2017

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of $N_\tau=4,6$ and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential by means of an expansion of the pressure. We use the expansion coefficients to calculate various fluctuations and correlations among hadronic charges. We find that the correlations reproduce the qualitative behavior of the resonance gas model below $T_c$ and start to agree with the free gas predictions for $T\gsim 1.5T_c$., Comment: Invited talk given at 'Strong and ElectroWeak Matter', Amsterdam, the Netherlands, 26-29 August 2008; 8 pages, 5 figures

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effect are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of $N_\tau=4,6$ and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential and present the isentropic equation of state on lines of constant entropy per baryon number., Comment: Invited talk given at the 3rd International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, 8-14 June 2008, Illa da Toxa, Spain; 7 pages, 6 figures

We discuss the Taylor expansion approach to non-zero baryon chemical potential ($\mu_B$) and present results on expanion coefficients of the pressure and energy density up to the 6-th order in $\mu_B$. Calculations have been performed with (2+1)-flavor of improved staggerd fermions (p4fat3) and almost physical masses on lattices with temporal extent of four and six time slices. We use the expansion coefficients to construct the isentropic equation of state on lines of constant entropy per baryon number and various different hadronic fluctuations. Furthermore, we estimate the radius of convegence of our expansion, which can be seen as a method to analyze the structure of the QCD phase diagram., Comment: Combined Contribution of two presentations given at the XXVI International Symposium on Lattice Field Theory, Williamsburg, Virginia, USA, 2008 July 14-19; 11 pages, 6 figures

We present results on baryon number, strangeness and electric charge fluctuations in QCD at non-zero density and temperature obtained from lattice calculations with almost physical quark masses. At vanishing chemical potential, i.e. under conditions almost realized at RHIC and the LHC, quartic fluctuations of net baryon number and strangeness are large in a narrow temperature interval characterizing the transition region from the low to the high temperature phase. Our results are based on Taylor expansions in light and strange quark chemical potentials, i.e. we rigorously compute corrections to bulk thermodynamic quantities at non vanishing chemical potential, by performing a Taylor expansion in $\mu/T$. We find non-monotonic behavior for the radius of convergence of this series, which could be a hint for a critical end-point in the ($T,\mu$)-plane., Comment: 4 pages, 5 figures; to appear in the proceedings of the 20th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions: Quark Matter 2008 (QM2008), Jaipur, India, Feb 4-10, 2008

The spatial string tension for 3+1 dimensional QCD at finite temperature is measured. The gauge configurations we re generated with two light and one heavier strange quark on lattices of size $16^3 4$ and $24^3 6$. This spatial string tension is compared with the string tension of the 3 dimensional pure gauge theory together with the temperature dependent 2-loop running coupling. Further comparison is made with predictions from dimensionally reduced effective theories.

We present results for screening masses of light and strange mesons in 2+1 flavour QCD using improved (p4fat3) staggered fermions on 6x24^3 lattices. We have studied the screening masses of scalar, pseudo-scalar, vector and axial-vector mesons along the line of constant physics, determined by a pion mass ~220 MeV and a kaon mass ~500 MeV. In order to investigate the cut-off and volume dependencies we have also performed studies of the meson screening correlators in the non-interacting theory using the p4 and the standard staggered discretizations.

We analyze the large-distance behaviour of static quark-anti-quark pair correlations in QCD. The singlet free energy is calculated and the entropy contribution to it is identified allowing us to calculate the excess internal energy. The free energy has a sharp drop in the critical region, leading to sharp peaks in both excess entropy and internal energy., Comment: talk given at Quark Matter 2006

We present results suggesting that magnetic monopoles can account for chiral symmetry breaking in abelian gauge theory. Full U(1) configurations from a lattice simulation are factorized into magnetic monopole and photon contributions. The expectation is computed using the monopole configurations and compared to results for the full U(1) configurations. It is shown that excellent agreement between the two values of is obtained if the effect of photons, which "dress" the composite operator psibarpsi, is included. This can be estimated independently by measurements of the physical fermion mass in the photon background., Comment: 14 pages REVTeX, including 5 figures