12,714 research outputs found

    Tachyonic crystals and the laminar instability of the perturbative vacuum in asymptotically free gauge theories

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    Lattice Monte Carlo studies in SU(3) gauge theory have shown that the topological charge distribution in the vacuum is dominated by thin coherent membranes of codimension one arranged in a layered, alternating-sign sandwich. A similar lamination of topological charge occurs in the 2D CPN1CP^{N-1} model. In holographic QCD, the observed topological charge sheets are naturally interpreted as D6D6 branes wrapped around an S4S_4.. With this interpretation, the laminated array of topological charge membranes observed on the lattice can be identified as a "tachyonic crystal", a regular, alternating-sign array of D6D6 and D6ˉ\bar{D6} branes that arises as the final state of the decay of a non-BPS D7D7 brane via the tachyonic mode of the attached string. In the gauge theory, the homogeneous, space-filling D7D7 brane represents the perturbative gauge vacuum, which is unstable toward lamination associated with a marginal tachyonic boundary perturbation cos(X/2α)\propto \cos(X/\sqrt{2\alpha'}). For the CPN1CP^{N-1} model, the cutoff field theory can be cast as the low energy limit of an open string theory in background gauge and tachyon fields Aμ(x)A_{\mu}(x) and λ(x)\lambda(x). This allows a detailed comparison with large NN field theory results and provides strong support for the tachyonic crystal interpretation of the gauge theory vacuum.Comment: 21 pages, 3 figure

    Small Instantons in CP1CP^1 and CP2CP^2 Sigma Models

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    The anomalous scaling behavior of the topological susceptibility χt\chi_t in two-dimensional CPN1CP^{N-1} sigma models for N3N\leq 3 is studied using the overlap Dirac operator construction of the lattice topological charge density. The divergence of χt\chi_t in these models is traced to the presence of small instantons with a radius of order aa (= 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 CP1CP^1 and CP2CP^2, leading to a divergent topological susceptibility in the continuum limit. For the \CP models with N>3N>3 the topological susceptibility is observed to scale properly with the mass gap. These larger NN 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 figure

    Spin Chains and Chiral Lattice Fermions

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    The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter's corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by fermionized nearest-neighbor Heisenberg spin chain operators. The transformation properties of the local lattice fermion operators under a boost provide a natural and precise way of generalizing the chiral structure of a continuum Dirac field to the lattice. The resulting formulation differs from both the Wilson and staggered (Kogut-Susskind) prescriptions. In particular, an axial Q5Q_5 rotation is sitewise local, while the vector charge rotation mixes nearest neighbors on even and odd sublattices.Comment: 3 pages, latex, no figure

    Long Range Topological Order, the Chiral Condensate, and the Berry Connection in QCD

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    Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a Berry connection, which is a gauge connection obtained from the phase of the electron wave function transported over momentum space rather than coordinate space. The phase of a closed Wilson loop of the Berry connection around the Brillouin zone defines a topological order parameter which labels discrete flux vacua. The conducting states are surface modes on the domain walls between discrete vacua. Evidence from large-NcN_c chiral dynamics, holographic QCD, and Monte Carlo observations has pointed to a picture of the QCD vacuum that is very similar to that of a topological insulator, with discrete quasivacua labelled by θ\theta angles that differ by mod 2π2\pi. In this picture, the domain walls are membranes of Chern-Simons charge, and the quark condensate consists of surface modes on these membranes, which are delocalized and thus support the long range propagation of Goldstone pions. The Berry phase in QED2 describes charge polarization of fermion-antifermion pairs, while in 4D QCD it describes the polarization of Chern-Simons membranes.Comment: 7 pages, no figures, talk presented at Lattice 201

    Anomaly Inflow and Membrane Dynamics in the QCD Vacuum

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    Large NcN_c 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 D6D6 branes in the holographic formulation of QCD based on IIA string theory. The polarizability of these membranes leads to a vacuum energy θ2\propto \theta^2, providing the origin of nonzero topological susceptibility. Here we show that the axial U(1) 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.Comment: 22 pages, 3 figure
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