189 research outputs found

### 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

### 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

### New algorithms and new results for strong coupling LQCD

We present and compare new types of algorithms for lattice QCD with staggered fermions in the limit
of infinite gauge coupling. These algorithms are formulated on a discrete spatial lattice but with continuous
Euclidean time. They make use of the exact Hamiltonian, with the inverse temperature beta
as the only input parameter. This formulation turns out to be analogous to that of a quantum spin
system. The sign problem is completely absent, at zero and non-zero baryon density. We compare
the performance of a continuous-time worm algorithm and of a Stochastic Series Expansion algorithm
(SSE), which operates on equivalence classes of time-ordered interactions. Finally, we apply the SSE
algorithm to a first exploratory study of two-flavor strong coupling lattice QCD, which is manageable
in the Hamiltonian formulation because the sign problem can be controlled

### 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

- â€¦