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

Analysis of penumbral eclipse data

Two days of data from the ATS-6 1976 eclipse season were analyzed to determine the effects of varying photoelectron flux on spacecraft potential. Particular emphasis was placed on the variation in potential as the satellite entered the earth's penumbra. Measurements from the AE-C satellite of the solar UV radiation were used to construct a model of atmospheric attenuation. This model was found to be consistent with direct measurements of the variations in photoelectron flux as Injun 5 passed into eclipse. Applying the model to the ATS-6 data gave the time dependency of the solar illumination/photoelectron flux as the satellite was eclipsed. This relationship, when combined with the ATS-6 measurements of satellite potential, revealed a nearly linear relation between the solar illumination/photoelectron flux and the logarithm of the satellite potential

Invariance of coarse median spaces under relative hyperbolicity

We show that, for finitely generated groups, the property of admitting a coarse median structure is preserved under relative hyperbolicity

Broken S3S_3 Neutrinos

Motivated by recent measurements which strongly support a nonzero reactor mixing angle $\theta_{13}$, we study a deviation from $S_3$ neutrino discrete symmetry by explicitly breaking the neutrino mass matrix with a general retrocirculant matrix. We show that nonzero $\theta_{13}$ and nonzero CP violation parameter $J_{CP}$ arise due to the difference between $y_2$ and $y_3$. We demonstrate that it is possible to obtain the experimentally favored results for neutrino masses and mixing angles from this mass matrix. Furthermore, we estimate the effective masses $m_{\beta}$ and $m_{\beta \beta}$ and total neutrino mass $\sum |m_i|$ predicted by this mass matrix.Comment: 10 pages, 6 figures, typos correcte