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

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

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

Precision Lattice Calculation of SU(2) 't Hooft loops

The [dual] string tension of a spatial 't Hooft loop in the deconfined phase of Yang-Mills theory can be formulated as the tension of an interface separating different Z_N deconfined vacua. We review the 1-loop perturbative calculation of this interface tension in the continuum and extend it to the lattice. The lattice corrections are large. Taking these corrections into account, we compare Monte Carlo measurements of the dual string tension with perturbation theory, for SU(2). Agreement is observed at the 2% level, down to temperatures O(10) T_c.Comment: 17 pages, 7 figures; reference added, typos correcte

QCD at zero baryon density

While the grand canonical partition function Z_{GC}(mu) with chemical potential mu explicitly breaks the Z_3 symmetry with the Dirac determinant, the canonical partition function at fixed baryon number Z_C(B) is manifestly Z_3-symmetric. We compare Z_{GC}(mu=0) and Z_C(B=0) formally and by numerical simulations, in particular with respect to properties of the deconfinement transition. Differences between the two ensembles, for physical observables characterising the phase transition, vanish with increasing lattice size. We show numerically that the free energy density is the same for both ensembles in the thermodynamic limit.Comment: Lattice2003(nonzero), 3 pages, 5 figure

Euclidean Dynamical Triangulation revisited: is the phase transition really first order?

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [3,4]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [3,4] an artificial harmonic potential was added to the action; in [4] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [6]. With these improved methods, on systems of size up to 64k 4-simplices, we confirm that the phase transition is first order.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Mean distribution approach to spin and gauge theories

We formulate self-consistency equations for the distribution of links in spin models and of plaquettes in gauge theories. This improves upon known mean-field, mean-link, and mean-plaquette approximations in such that we self-consistently determine all moments of the considered variable instead of just the first. We give examples in both Abelian and non-Abelian cases.Comment: 11 pages, 8 figure

Scale hierarchy in high-temperature QCD

Because of asymptotic freedom, QCD becomes weakly interacting at high temperature: this is the reason for the transition to a deconfined phase in Yang-Mills theory at temperature $T_c$. At high temperature $T \gg T_c$, the smallness of the running coupling $g$ induces a hierachy betwen the "hard", "soft" and "ultrasoft" energy scales $T$, $g T$ and $g^2 T$. This hierarchy allows for a very successful effective treatment where the "hard" and the "soft" modes are successively integrated out. However, it is not clear how high a temperature is necessary to achieve such a scale hierarchy. By numerical simulations, we show that the required temperatures are extremely high. Thus, the quantitative success of the effective theory down to temperatures of a few $T_c$ appears surprising a posteriori.Comment: 7 pages, 8 figures. Talk presented at 31st International Symposium on Lattice Field Theory (LATTICE 2013), July 29 - August 3, 2013, Mainz, German