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 consider quantum entanglement between gauge fields in some region of space A and its complement B. It is argued that the Hilbert space of physical states of gauge theories cannot be decomposed into a direct product HA ⊗ HB of Hilbert spaces of states localized in A and B. The reason is that elementary excitations in gauge theories -electric strings -are associated with closed loops rather than points in space, and there are closed loops which belong both to A and B. Direct product structure and hence the reduction procedure with respect to the fields in B can only be defined if the Hilbert space of physical states is extended by including the states of electric strings which can open on the boundary of A. The positions of string endpoints on this boundary are the additional degrees of freedom which also contribute to the entanglement entropy. We explicitly demonstrate this for the three-dimensional Z2 lattice gauge theory both numerically and using a simple trial ground state wave function. The entanglement entropy appears to be saturated almost completely by the entropy of string endpoints, thus reminding of a "holographic principle" in quantum gravity and AdS/CFT correspondence.Geometric entanglement entropy [1, 2, 3] of confining gauge theories has recently become a subject of extensive studies, mostly due to the discovery of its non-analytical behavior with respect to the size of the region. This non-analyticity was first predicted in the framework of AdS/CFT correspondence in [4,5], and then within the Migdal-Kadanoff approximation in lattice gauge theories [6]. Finally, a signature of nonanalytic behavior of entanglement entropy was found in numerical simulations of SU (2) lattice gauge theory [7].In order to define the geometric entanglement entropy of some region A, one should represent the Hilbert space H of the field theory under consideration as a direct product of Hilbert spaces H A and H B of states localized in A and its complement B [8]: H = H A ⊗ H B . For instance, for scalar field theory the spaces H A and H B can be constructed by acting on some proper initial state with field operators localized within A and B. In other words, elementary excitations of scalar fields are associated with points in space, and any point can be classified as belonging either to A or B (except for the set of points on the boundary, which has zero measure). One then defines the reduced density matrix for the fields in A as a partial trace of the density matrix of the ground state |0 of the theory over H B :ρ A = Tr B |0 0| . Geometric entanglement entropy S [A] is the von Neumann entropy of the reduced density matrixρ A [8]:However, in none of the works [4,5,6,7] such a direct * Electronic address: buividovich@tut.by † Electronic address: polykarp@itep.ru product structure was explicitly constructed for gauge theories or even used. The papers [4,5] mainly rely on the conjecture of [9] which relates the entanglement entropy of conformal field theories living on the boundary of AdS space with certain minimal hypersu...

We report on the results of the first-principles numerical study of spontaneous breaking of chiral (sublattice) symmetry in suspended monolayer graphene due to electrostatic interaction, which takes into account the screening of Coulomb potential by electrons on σ orbitals. In contrast to the results of previous numerical simulations with unscreened potential, we find that suspended graphene is in the conducting phase with unbroken chiral symmetry. This finding is in agreement with recent experimental results by the Manchester group [D. C. Elias et al., Nat. Phys. 7, 701 (2011); A. S. Mayorov et al., Nano Lett. 12, 4629 (2012)]. Further, by artificially increasing the interaction strength, we demonstrate that suspended graphene is quite close to the phase transition associated with spontaneous chiral symmetry breaking, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.