12,714 research outputs found

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

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 $CP^{N-1}$ model.
In holographic QCD, the observed topological charge sheets are naturally
interpreted as $D6$ branes wrapped around an $S_4$.. 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
$D6$ and $\bar{D6}$ branes that arises as the final state of the decay of a
non-BPS $D7$ brane via the tachyonic mode of the attached string. In the gauge
theory, the homogeneous, space-filling $D7$ brane represents the perturbative
gauge vacuum, which is unstable toward lamination associated with a marginal
tachyonic boundary perturbation $\propto \cos(X/\sqrt{2\alpha'})$. For the
$CP^{N-1}$ model, the cutoff field theory can be cast as the low energy limit
of an open string theory in background gauge and tachyon fields $A_{\mu}(x)$
and $\lambda(x)$. This allows a detailed comparison with large $N$ 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 $CP^1$ and $CP^2$ Sigma Models

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 figure

### Spin Chains and Chiral Lattice Fermions

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 $Q_5$ 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

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-$N_c$ 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 $\theta$ angles that differ by mod $2\pi$. 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

Large $N_c$ 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 $D6$ branes in the holographic
formulation of QCD based on IIA string theory. The polarizability of these
membranes leads to a vacuum energy $\propto \theta^2$, 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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