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 CP1CP^1 and CP2CP^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

Casimir force for cosmological domain walls

We calculate the vacuum fluctuations that may affect the evolution of cosmological domain walls. Considering domain walls, which are classically stable and have interaction with a scalar field, we show that explicit symmetry violation in the interaction may cause quantum bias that can solve the cosmological domain wall problem.Comment: 15 pages, 2figure

Numerical Studies of the Gauss Lattice Problem

The difference between the number of lattice points N(R) that lie in x^2 + y^2 ≤ R^2 and the area of that circle, d(R) = N(R) - πR^2, can be bounded by |d(R)| ≤ KR^θ. Gauss showed that this holds for θ = 1, but the least value for which it holds is an open problem in number theory. We have sought numerical evidence by tabulating N(R) up to R ≈ 55,000. From the convex hull bounding log |d(R)| versus log R we obtain the bound θ ≤ 0.575, which is significantly better than the best analytical result θ ≤ 0.6301 ... due to Huxley. The behavior of d(R) is of interest to those studying quantum chaos

Circuit protects regulated power supply against overload current

Sensing circuit in which a tunnel diode controls a series regulator transistor protects a low voltage transistorized dc regulator from damage by excessive load currents. When a fault occurs, the faulty circuit is limited to a preset percentage of the current when limiting first occurs

Magnetically actuated tuning method for Gunn oscillators

A tunable microwave generator based on the Gunn effect is disclosed. The generator includes a semiconductor material which exhibits the Gunn effect when current flows between anode and cathode end contacts. The material has a plurality of sides each with a scratch at a different distance from the anode contact. A magnetic field is produced by a magnet placed about the semiconductor field. The Lorentz force produced as a function of the current flow and the magnetic field drive the electrons to the surface of one of the sides to cause nucleation to occur at the scratch. A domain formed thereat travels to the anode contact to provide pulses at a frequency which is related to the distance between the scratch and the anode contact

Dimension Four Wins the Same Game as the Standard Model Group

In a previous article Don Bennett and I looked for,found and proposed a game in which the Standard Model group S(U(2)XU(3)) gets singled out as the "winner". Here I propose to extend this "game" to construct a corresponding game between different potential dimensions for space time. The idea is to formulate how the same competition as the one between the potential gauge groups would run out, if restricted to the potential Lorentz or Poincare groups achievable for different dimensions of space time d. The remarkable point is that it is the experimental dimension of space time 4 which wins. So the same function defined over Lie groups seems to single out both the gauge group and the space time dimension in nature. This seems a rather strange coincidence unless there is really some similar physics behind.Comment: After introducing some more review o the previous article the historical stuff was moved into an appendi