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Both theoretical arguments and Monte Carlo observations indicate that the topological structure of the QCD vacuum consists of a laminated array of extended, coherent codimension-one membranes of alternating sign. Large-$N_c$ arguments, supported by gauge/string holography, indicate that these membranes are domain walls which separate discrete "flux vacua" with values of the topological $\theta$ parameter which differ by $\pm 2\pi$. This exposes a close analogy with 2D U(1) gauge theory, where $\theta$ can be interpreted as electric polarization, and the domain walls are pointlike charged particles. In 4D QCD, the $\theta$ parameter represents background Ramond-Ramond flux, which can be interpreted as a polarization of the charged membranes in the vacuum. In this framework, the chiral condensate is formed from the quark surface modes on the membranes. Massless Goldstone boson propagation takes place due to a coordination between bulk oscillations of the polarization field $\theta$ and the surface currents represented by the Chern-Simons 3-form on the brane surface. This coordination is enforced by overall gauge invariance which imposes an anomaly inflow constraint between bulk and surface currents., Comment: 6 pages, Talk presented at Chiral Dynamics Workshop, Jefferson Lab, Aug. 2012

The Witten-Sakai-Sugimoto construction of holographic QCD in terms of D4 color branes and D8 flavor branes in type IIA string theory is used to investigate the role of topological charge in the chiral dynamics of quarks in QCD. The QCD theta term arises from a compactified 5-dimensional Chern-Simons term on the D4 branes. This term couples the QCD topological charge to the Ramond-Ramond $U(1)$ gauge field of IIA string theory. The nonzero topological susceptibility of pure-glue QCD can be attributed to the presence of D6 branes, which constitute magnetic sources of the RR gauge field. The topological charge of QCD is required, by an anomaly inflow argument, to coincide in space-time with the intersection of the D6 branes and the D4 color branes. This clarifies the relation between D6 branes and the coherent, codimension-one topological charge membranes observed in QCD Monte Carlo calculations. Using open-string/closed-string duality, we interpret a quark loop (represented by a D4-D8 open string loop) in terms of closed-string exchange between color and flavor branes. The role of the RR gauge field in quark-antiquark annihilation processes is discussed. RR exchange in the s-channel generates a 4-quark contact term which produces an $\eta'$ mass insertion and provides an explanation for the observed spin-parity structure of the OZI rule. The $(\log {\rm Det\;U})^2$ form of the $U(1)$ anomaly emerges naturally. RR exchange in the t-channel of the $q\overline{q}$ scattering amplitude produces a Nambu-Jona Lasinio interaction which may provide a mechanism for spontaneous breaking of $SU(N_f)\times SU(N_f)$., Comment: 20 pages, 7 figures

Monte Carlo studies of $CP^{N-1}$ sigma models have shown that the structure of topological charge in these models undergoes a sharp transition at $N=N_c\approx 4$. For $NN_c$ it is dominated by extended, thin, 1-dimensionally coherent membranes of topological charge, which can be interpreted as domain walls between discrete quasi-stable vacua. These vacua differ by a unit of background electric flux. The transition can be identified as the delocalization of topological charge, or "instanton melting," a phenomenon first suggested by Witten to resolve the conflict between instantons and large $N$ behavior. Implications for $QCD$ are discussed., Comment: 7 pages, 3 figures. Talk presented at Lattice 2008, Williamsburg, VA

Recent work by Armoni, Shifman, and Veneziano suggests a large-N equivalence between supersymmetric Yang-Mills Theory and one-flavor QCD. One consequence of this "orientifold projection" is that scalar and pseudoscalar mesons in one-flavor QCD should have degenerate mass since they lie within the same Wess-Zumino supermultiplet. We use lattice calculations to investigate the mass shifts caused by "double-hairpin" annihilation diagrams in quenched QCD to test for this degeneracy. Similar quark-antiquark annihilation processes are studied in the 2-dimensional CP(N-1) model with quenched fermions., 7 pages, 2 figures (2 figure files), PoS style, Lattice 2006 Poster (Beyond QCD)

Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. Studies of localization properties of Dirac eigenmodes have also shown evidence for the delocalization of low-lying modes on effectively 3-dimensional surfaces. In this talk, I review some theoretical ideas which suggest the possibility of 3-dimensionally coherent topological charge structure in 4-dimensional gauge theory and provide a possible interpretation of the observed structure. I begin with Luscher's ``Wilson bag'' integral over the 3-index Chern-Simons tensor. The analogy with a Wilson loop as a charged world line in 2-dimensional $CP^{N-1}$ sigma models suggests that the Wilson bag surface represents the world volume of a physical membrane. The large-N chiral Lagrangian arguments of Witten also indicate the existence of multiple ``k-vacuum'' states with discontinuous transitions between k-vacua at $\theta=$ odd multiples of $\pi$. The domain walls between these vacua have the properties of a Wilson bag surface. Finally, I review the AdS/CFT duality view of $\theta$ dependence in QCD. The dual realtionship between topological charge in gauge theory and Ramond-Ramond charge in type IIA string theory suggests that the coherent topological charge sheets observed on the lattice are the holographic image of wrapped D6 branes., Comment: 15 pages, 3 figures. Talk presented at Lattice 2006, Tucson, AZ, July 23-27, 2006

The anomalous scaling behavior of the topological susceptibility $\chi_t$ in two-dimensional $CP^{N-1}$ sigma models for $N\leq 3$ is studied using the overlap Dirac operator construction of the lattice topological charge density. The divergence of $\chi_t$ in these models is traced to the presence of small instantons with a radius of order $a$ (= lattice spacing), which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of L\"{u}scher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in $CP^1$ and $CP^2$, leading to a divergent topological susceptibility in the continuum limit. For the $\CP$ models with $N>3$ the topological susceptibility is observed to scale properly with the mass gap. These larger $N$ models are not dominated by instantons, but rather by coherent, one-dimensional regions of topological charge which can be interpreted as domain wall or Wilson line excitations and are analogous to D-brane or ``Wilson bag'' excitations in QCD. In Lorentz gauge, the small instantons and Wilson line excitations can be described, respectively, in terms of poles and cuts of an analytic gauge potential., Comment: 33 pages, 12 figures

In an effort to clarify the significance of the recent observation of long-range topological charge coherence in QCD gauge configurations, we study the local topological charge distributions in two-dimensional $CP^{N-1}$ sigma models, using the overlap Dirac operator to construct the lattice topological charge. We find long-range sign coherence of topological charge along extended one-dimensional structures in two-dimensional spacetime. We discuss the connection between the long range topological structure found in $CP^{N-1}$ and the observed sign coherence along three-dimensional sheets in four-dimensional QCD gauge configurations. In both cases, coherent regions of topological charge form along membrane-like surfaces of codimension one. We show that the Monte Carlo results, for both two-dimensional and four-dimensional gauge theory, support a view of topological charge fluctuations suggested by Luscher and Witten. In this framework, the observed membranes are associated with boundaries between ``k-vacua,'' characterized by an effective local value of $\theta$ which jumps by $\pm 2\pi$ across the boundary., Comment: 26 pages

The recently observed long-range coherent structure of topological charge fluctuations in QCD is compared with theoretical expectations based on the AdS/CFT brane construction of nonsupersymmetric gauge theory by Witten. Similar observations of coherent topologicalcharge structure in 2D $CP^{N-1}$ sigma models are interpreted in terms of Wilson lines representing world lines of screened electric charges. The analogy between 2D U(1) and 4D Yang-Mills theory leads to the interpretation of the observed coherent sheets of topological charge in QCD as screened ``Wilson bags'' first suggested by Luscher. The duality between the Wilson bag surface and a wrapped 6-brane in IIA string theory is discussed. The complete screening of the force between bag surfaces for integer values of the bag charge $\theta/2\pi$ corresponds to the observation by Polchinski that the net force between d-branes from closed string exchange vanishes for quantized values of Ramond-Ramond charge., Comment: Talk presented at Lattice 2005

We consider the lattice topological charge density introduced by Hasenfratz, Laliena and Niedermayer and propose its eigenmode expansion as a tool to investigate the structure of topological charge fluctuations in QCD. The resulting effective density is built from local chiralities studied previously. At every order of the expansion the density exactly sums up to the global topological charge, and the leading term describes the maximally smooth space-time distribution of charge relevant for propagating light fermions. We use this framework to demonstrate our previous suggestion that the bulk of topological charge in QCD does not effectively appear in the form of quantized unit lumps. Our conclusion implies that it is unlikely that the mixing of "would-be" zeromodes associated with such lumps is the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. We also present first results quantitatively characterizing the space-time behavior of effective densities. For coherent fluctuations contained in spherical regions we find a continuous distribution of associated charges essentially ending at ~0.5., 5 pages, 4 figures, RevTex; v2: typo in eq. (3) fixed; v3: References added, minor cosmetic changes, unchanged conclusions, published version

The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft "would-be" zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological "would-be" zeromodes could be associated., Comment: Presented by I. Horvath at the NATO Advanced Research Workshop "Confinement, Topology, and other Non-Perturbative Aspects of QCD", January 21-27, 2002, Stara Lesna, Slovakia. 12 pages, 6 figures, uses crckapb.sty

The OZI rule is prominent in hadronic phenomena only because OZI violation is typically an order of magnitude smaller than expected from large N_c arguments. With its standard ^3P_0 pair creation operator for hadronic decays by flux tube breaking, the quark model respects the OZI rule at tree level and exhibits the cancellations between OZI-violating meson loop diagrams required for this dramatic suppression. However, if the quark model explanation for these cancellations is correct, then OZI violation would be expected to be large in the nonet with the same quantum numbers as the pair creation operator: the 0^{++} mesons. Experiment is currently unable to identify these mesons, but we report here on a lattice QCD calculation which confirms that the OZI rule arises from QCD in the vector and axial vector mesons as observed, and finds a large violation of the rule in the scalar mesons as anticipated by the quark model. In view of this result, we make some remarks on possible connections between the ^3P_0 pair creation model, scalar mesons, and the U_A(1) anomaly responsible for the large OZI violation which drives the \eta' mass. In particular, we note that our result favors the large N_c and not the instanton interpretation of the solution to the \eta' mass problem., Comment: 29 pages, 9 figures; the original version of this paper had a sign error which affects the interpretation of some of the results; some new references added and typos corrected

Preliminary results of a study of quenched chiral logarithms at beta=5.7 are presented. Four independent determinations of the quenched chiral log parameter delta are obtained. Two of these are from estimates of the eta-prime mass, one from the residue of the hairpin diagram and the other from the topological susceptibility combined with the Witten-Veneziano formula. The other two determinations of delta are from measurement of virtual eta-prime loop effects in mpi^2 vs. quark mass and in the chiral behavior of the pseudoscalar decay constant. All results are consistent with delta=.080(15). The expected absence of quenched chiral logs in the axial-vector decay constant is also observed., Talk presented at Lattice '99 by H. Thacker

For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or Lorentz-frame independence of the theory, which is only recovered in the continuum limit. The Baxter 8-vertex model may be interpreted as a particular discretization of a self-interacting massive Dirac fermion theory in two dimensions (the massive Thirring model). Here it is shown that, in the 8-vertex/massive Thirring model, the Lorentz frame independence of the theory remains undisturbed on the lattice. The only effect of the discretization is to compactify the manifold of Lorentz frames. The relationship between this lattice Lorentz symmetry and the Yang-Baxter relations is discussed., 15 pages, no figures

The calculation of the eta-prime hairpin diagram is carried out in the modified quenched approximation (MQA) in which the lattice artifact which causes exceptional configurations is removed by shifting observed poles at kappa, Comment: 3 pages, 3 postscript figures

The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional integral is shown to be extremely compicated, with multiple branch points and cuts. The connection of lattice topological charge and exactly real eigenmodes is explored using cooling techniques. The lattice volume and spacing dependence of these modes is studied, as is the effect of clover improvement of the action. A recently proposed modified quenched approximation is applied to the study of meson correlators, and the results compared with both naive quenched and full dynamical calculations of the same quantity., Comment: 34 pages (Latex) plus 9 embedded figures; title changed

Limits on the size of quenched chiral logs in the pion mass for Wilson fermions are investigated. The smallness of chiral logs is shown to be a result of the suppression of the hairpin diagram for small $p^2$, such that the value of the hairpin on the pion mass shell is much smaller than the physical $m_{��'}^2$. A direct calculation of the topological susceptibility from the same data gives $m_{��'}\approx 1$ GeV.