Lattice QCD Thermodynamics on the Grid

We describe how we have used simultaneously ${\cal O}(10^3)$ nodes of the EGEE Grid, accumulating ca. 300 CPU-years in 2-3 months, to determine an important property of Quantum Chromodynamics. We explain how Grid resources were exploited efficiently and with ease, using user-level overlay based on Ganga and DIANE tools above standard Grid software stack. Application-specific scheduling and resource selection based on simple but powerful heuristics allowed to improve efficiency of the processing to obtain desired scientific results by a specified deadline. This is also a demonstration of combined use of supercomputers, to calculate the initial state of the QCD system, and Grids, to perform the subsequent massively distributed simulations. The QCD simulation was performed on a $16^3\times 4$ lattice. Keeping the strange quark mass at its physical value, we reduced the masses of the up and down quarks until, under an increase of temperature, the system underwent a second-order phase transition to a quark-gluon plasma. Then we measured the response of this system to an increase in the quark density. We find that the transition is smoothened rather than sharpened. If confirmed on a finer lattice, this finding makes it unlikely for ongoing experimental searches to find a QCD critical point at small chemical potential

Vortex free energies in SO(3) and SU(2) lattice gauge theory

Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement-deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).Comment: 3 pages, 2 figures, talk presented at Lattice2002(topology

Localization properties of fermions and bosons

The topological structure of the QCD vacuum can be probed by monitoring the spatial localization of the low-lying Dirac eigenmodes. This approach can be pursued on the lattice, and unlike the traditional one requires no smoothing of the gauge field. I review recent lattice studies, attempting to extract a consistent description. What emerges is a picture of the vacuum as a ``topological sandwich'' of alternating, infinitely thin 3d layers of opposite topological charge, as originally seen in direct measurements of the topological charge density.Comment: Invited talk at "Quark Confinement and the Hadron Spectrum VII", Azores, Portugal, 2-7 September 2006. 7 pages, 11 figures. To appear in the Proceedings. Small changes; references adde

Electric and Magnetic Fluxes in SU(2) Yang-Mills Theory

We measure the free energies in SU(2) of static fundamental charges and center monopoles. Dual to temporal center fluxes, the former provide a well-defined (dis)order parameter for deconfinement. In contrast, the monopole free energies vanish in the thermodynamic limit at all temperatures and are thus irrelevant for the transition.Comment: 3 pages, LaTeX2e (espcrc2.sty), 4 figures (epsfig), for Lattice2002(topology

Laplacian gauge and instantons

We exhibit the connection between local gauge singularities in the Laplacian gauge and topological charge, which opens the possibility of studying instanton excitations without cooling. We describe our version of Laplacian gauge-fixing for SU(N).Comment: Lattice 2000 (Topology and Vacuum), 4 pages, 3 figures -- cosmetic change

Gauge-invariant signatures of spontaneous gauge symmetry breaking by the Hosotani mechanism

The Hosotani mechanism claims to achieve gauge-symmetry breaking, for instance $SU(3) \to SU(2)\times U(1)$. To verify this claim, we propose to monitor the stability of a topological defect stable under a gauge subgroup but not under the whole gauge group, like a $U(1)$ flux state or monopole in the case above. We use gauge invariant operators to probe the presence of the topological defect to avoid any ambiguity introduced by gauge fixing. Our method also applies to an ordinary gauge-Higgs system.Comment: 7 pages, 6 figures, talk presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23 - 28 June, 2014, Columbia University New York, N

Deconfinement transition in 2+1-dimensional SU(4) lattice gauge theory

A missing piece is added to the Svetitsky-Yaffe conjecture. The spin model in the same universality class as the (2+1)d SU(4) theory, the 2d Ashkin-Teller model, has a line of continuously varying critical exponents. The exponents measured in the gauge theory correspond best to the Potts point on the Ashkin-Teller line.Comment: Lattice2003(topology), 3 pages, 5 figure

Laplacian Center Vortices

I present a unified picture of center vortices and Abelian monopoles. Both appear as local gauge ambiguities in the Laplacian Center Gauge. This gauge is constructed for a general SU(N) theory. Numerical evidence is presented, for SU(2) and SU(3), that the projected $Z_N$ theory confines with a string tension similar to the non-Abelian one.Comment: 9 pages, 5 figures; talk presented at "Confinement 2000", Osaka, March 200

Finite density QCD with a canonical approach

We present a canonical method where the properties of QCD are directly obtained as a function of the baryon density rho, rather than the chemical potential mu. We apply this method to the determination of the phase diagram of four-flavor QCD. For a pion mass m_pi \sim 350 MeV, the first-order transition between the hadronic and the plasma phase gives rise to a co-existence region in the T-rho plane, which we study in detail, including the associated interface tension. We obtain accurate results for systems containing up to 30 baryons and quark chemical potentials mu up to 2 T. Our T-mu phase diagram agrees with the literature when mu/T \lesssim 1. At larger chemical potential, we observe a ``bending down'' of the phase boundary. We compare the free energy in the confined and deconfined phase with predictions from a hadron resonance gas and from a free massless quark gas respectively.Comment: 6 pages, 9 figures, proceedings of "Workshop on Computational Hadron Physics", Cyprus, Sept. 200