We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

We study correlations between center vortices and the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. In particular we address a puzzle raised some years ago by Gattnar et al. [ Nucl. Phys. B716, 105 (2005)], who noted that the low-lying Dirac eigenmodes required for chiral symmetry breaking do not appear to be present in center-projected configurations. We show that the low-lying modes are in fact present in the staggered (asqtad) formulation, but not in the overlap and “chirally improved” formulations, and suggest a reason for this difference. We also confirm and extend the results of Kovalenko et al. [ Phys. Lett. B 648, 383 (2007)], showing that there is a correlation between center vortex locations, and the scalar density of low-lying Dirac eigenmodes derived from unprojected configurations. This correlation is strongest at points which are associated, in the vortex picture, with nonvanishing topological charge density, such as vortex intersection and writhing points. We present supporting evidence that the lowest Dirac eigenmodes, in both asqtad and overlap formulations, have their largest concentrations in pointlike regions, rather than on submanifolds of higher dimensionality.

We calculate the chameleon field potential for ultracold neutrons bouncing on top of one, or between two, neutron mirrors in the gravitational field of the Earth. For the resulting nonlinear equations of motion, we give approximate analytical solutions and compare them with exact numerical ones for which we propose the analytical fit. The obtained solutions may be used for the quantitative analysis of contributions of a chameleon field to the transition frequencies of quantum states of ultracold neutrons bound in the gravitational field of the Earth.

We investigate the chiral properties of near-zero modes for thick classical center vortices in $SU(2)$ lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.

We consider “double-winding” Wilson loops in SU(2) gauge theory. These are contours which wind once around a loop $C_1$ and once around a loop $C_2$, where the two co-planar loops share one point in common, and where $C_1$ lies entirely in (or is displaced slightly from) the minimal area of $C_2$. We discuss the expectation value of such double-winding loops in Abelian confinement pictures, where the spatial distribution of confining Abelian fields is controlled by either a monopole Coulomb gas, a caloron ensemble, or a dual Abelian Higgs model, and argue that in such models an exponential falloff in the sum of areas $A_1+A_2$ is expected. In contrast, in a center vortex model of confinement, the behavior is an exponential falloff in the difference of areas $A_2-A_1$. We compute such double-winding loops by lattice Monte Carlo simulation, and find that the area law falloff follows a difference-in-areas law. The conclusion is that even if confining gluonic field fluctuations are, in some gauge, mainly Abelian in character, the spatial distribution of those Abelian fields cannot be the distribution predicted by the simple monopole gas, caloron ensemble, or dual Abelian Higgs actions, which have been used in the past to explain the area law falloff of Wilson loops.