Impact of Dynamical Fermions on QCD Vacuum Structure

We examine how dynamical fermions affect both the UV and infrared structure of the QCD vacuum. We consider large $28^3 \times 96$ lattices from the MILC collaboration, using a gluonic definition of the topological charge density, founded on a new over-improved stout-link smearing algorithm. The algorithm reproduces established results from the overlap formalism and is designed to preserve nontrivial topological objects including instantons. At short distances we focus on the topological charge correlator, , where negative values at small $x$ reveal a sign-alternating layered structure to the topological-charge density of the QCD vacuum. We find that the magnitudes of the negative dip in the correlator and the positive $$ contact term are both increased with the introduction of dynamical fermion degrees of freedom. This is in accord with expectations based on charge renormalization and the vanishing of the topological susceptibility in the chiral limit. At large distances we examine the extent to which instanton-like objects are found on the lattice, and how their distributions vary between quenched and dynamical gauge fields. We show that dynamical gauge fields contain more instanton-like objects with an average size greater than in the quenched vacuum. Finally, we directly visualize the topological charge density in order to investigate the effects of dynamical sea-quark degrees of freedom on topology.Comment: 9 pages, 8 figure

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Ethane-1,2-diylbis(methyl­phosphinic acid)

In the title compound, C4H12O4P2, there are two crystallographically independent half-mol­ecules in the asymmetric unit, both molecules lying on centres of symmetry. Each mol­ecule is connected on both sides to neighbouring mol­ecules via strong O—H⋯O hydrogen bonds. The –POOH groups accept and donate one hydrogen bond in interactions with the neighbouring –POOH group of the adjacent mol­ecule, to give one-dimensional chains along [10]. As each phosphinic acid group donates and accepts one hydrogen bond, the connection between the mol­ecules is best described by a ring motif which can be classified by the Etter symbol R 2 2(8)

Writhe of center vortices and topological charge -- an explicit example

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore, the time evolution of the vortex line discussed in this work can be viewed as a gif movie, available for download by following the PostScript link below -- watch for the cute feature at the self-intersection poin

Salamanca, Ávila y Segovia

Copia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 2009-201

Dressed Polyakov loop and flavor dependent phase transitions

The chiral condensate and dressed Polyakov loop at finite temperature and density have been investigated in the framework of Nf = 2+1 Nambu-Jona-Lasinio (NJL) model with two degenerate u, d quarks and one strange quark. In the case of explicit chiral symmetry breaking with physical quark masses, it is found that the phase transitions for light u, d quarks and s quark are sequentially happened, and the separation between the transition lines for different flavors becomes wider and wider with the increase of baryon density. For each flavor, the pseudo-critical temperatures for chiral condensate and dressed Polyakov loop differ in a narrow transition range in the lower baryon density region, and the two transitions coincide in the higher baryon density region.Comment: 9 pages, 9 figures; Version accepted in Phys. Rev.

Polyakov loops and spectral properties of the staggered Dirac operator

We study the spectrum of the staggered Dirac operator in SU(2) gauge fields close to the free limit, for both the fundamental and the adjoint representation. Numerically we find a characteristic cluster structure with spacings of adjacent levels separating into three scales. We derive an analytical formula which explains the emergence of these different spectral scales. The behavior on the two coarser scales is determined by the lattice geometry and the Polyakov loops, respectively. Furthermore, we analyze the spectral statistics on all three scales, comparing to predictions from random matrix theory.Comment: 11 pages, 25 figures; v2: minor changes, as published in Phys. Rev.

Groping in the Dark: The First Decade of Global Modelling

This book is the real life history of global modelling. It is concerned with the major models and those who make them, the whole craft of modelling, and their principal results. A feature is the honesty, candour, and clarity with which the authors discuss what global modelling taught them about modelling and what it taught them about the world. It could be described as a book on the sociology of a new science struggling with problems too large for the participants but too important to ignore. This book is written for those who make complex models of complex social systems, those who have to make these systems work, and those who live in and care about the social systems that modellers make and about which decision makers make decisions