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There is considerable evidence, based on large Nc chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the topological θ parameter jumps by ±2π. This scenario is realized in a 2D U(1) gauge theory, the CPN-1 sigma model, where a pointlike charge is a domain wall, and θ describes the background electric flux and the polarization of charged pairs in the vacuum. The transition between discrete θ vacua occurs via the transport of integer units of charge between the two spatial boundaries of the domain. We show that this screening process, and the role of θ as an order parameter describing electric polarization, are naturally formulated in terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background gauge field. This formulation is similar to the Berry phase description of electric polarization and quantized charge transport in topological insulators. The Bloch waves are quasiperiodic superpositions of localized Dirac zero modes and the charge transport takes place coherently via topological charge-induced spectral flow. The adiabatic spectral parameter becomes the Bloch wave momentum, which defines a Berry connection around the Brillouin zone of the zero mode band. It describes the local polarization of vacuum pairs, analogous to its role in topological insulator theory. In 4D Yang-Mills theory, the θ domain walls are 2 + 1-dimensional Chern-Simons membranes, and the θ parameter describes the local polarization of brane-antibrane pairs. The topological description of polarization in 2D U(1) gauge theory generalizes to membrane polarization in 4D QCD by exploiting a relationship between the Berry connection and the gauge cohomology structure encoded in the descent equations of 4D Yang-Mills theory. [ABSTRACT FROM AUTHOR]

Large Nc and holographic arguments, as well as Monte Carlo results, suggest that the topological structure of the QCD vacuum is dominated by codimension-one membranes which appear as thin dipole layers of topological charge. Such membranes arise naturally as D6-branes in the holographic formulation of QCD based on IIA string theory. The polarizability of these membranes leads to a vacuum energy a θ2, providing the origin of nonzero topological susceptibility. Here we show that the axial U(l) anomaly can be formulated as anomaly inflow on the brane surfaces. A 4D gauge transformation at the brane surface separates into a 3D gauge transformation of components within the brane and the transformation of the transverse component. The in-brane gauge transformation induces currents of an effective Chern-Simons theory on the brane surface, while the transformation of the transverse component describes the transverse motion of the brane and is related to the Ramond-Ramond closed string field in the holographic formulation of QCD. The relation between the surface currents and the transverse motion of the brane is dictated by the descent equations of Yang-Mills theory. [ABSTRACT FROM AUTHOR]

The structure of topological charge fluctuations in the QCD vacuum is strongly restricted by the spectral negativity of the Euclidean correlator for x ≠ 0 and the presence of a positive contact term. Some examples are considered which illustrate the physical origin of these properties. [Copyright &y& Elsevier]

We present results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched QCD at two values of lattice spacing, β = 5.7 and 5.9, with clover-improved Wilson fermions. The study of the chiral limit is facilitated by the pole-shifting ansatz of the modified quenched approximation. Pseudoscalar masses and decay constants are determined as a function of quark mass and quenched chiral log effects are estimated. A study of the flavor singlet ν′ hairpin diagram yields a precise determination of the ν′ mass insertion. The corresponding value of the quenched chiral log parameter b is compared with the observed QCL effects. Removal of QCL effects from the scalar propagator allows a determination of the mass of the lowest lying isovector scalar qq meson. [Copyright &y& Elsevier]