Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.Comment: 41 page

Global entanglement in multiparticle systems

We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin-1/2 particles. By evaluating it for three particle states, for eigenstates of the one dimensional Heisenberg antiferromagnet and on quantum error correcting code subspaces, we illustrate the extent to which it quantifies global entanglement. We also apply it to track the evolution of entanglement during a quantum computation.Comment: 9 pages, plain TeX, 1 PostScript figure included with epsf.tex (ignore the under/overfull \vbox error messages); for related work see http://math.ucsd.edu/~dmeyer/research.html or http://www.math.ucsd.edu/~nwallach

Kaluza-Klein supergravity on AdS_3 x S^3

We construct a Chern-Simons type gauged N=8 supergravity in three spacetime dimensions with gauge group SO(4) x T_\infty over the infinite dimensional coset space SO(8,\infty)/(SO(8) x SO(\infty)), where T_\infty is an infinite dimensional translation subgroup of SO(8,\infty). This theory describes the effective interactions of the (infinitely many) supermultiplets contained in the two spin-1 Kaluza-Klein towers arising in the compactification of N=(2,0) supergravity in six dimensions on AdS_3 x S^3 with the massless supergravity multiplet. After the elimination of the gauge fields associated with T_\infty, one is left with a Yang Mills type gauged supergravity with gauge group SO(4), and in the vacuum the symmetry is broken to the (super-)isometry group of AdS_3 x S^3, with infinitely many fields acquiring masses by a variant of the Brout-Englert-Higgs effect.Comment: LaTeX2e, 24 pages; v2: references update

A Spectroscopic Binary at the M/L Transition

We report the discovery of a single-lined spectroscopic binary with an Ultra Cool Dwarf (UCD) primary with a spectral type between M8 and L0.5. This system was discovered during the course of an ongoing survey to monitor L dwarfs for radial velocity variations and is the first known small separation (a<1 AU) spectroscopic binary among dwarfs at the M/L transition. Based on radial-velocity measurements with a typical precision of 300 m/s we estimate the orbital parameters of this system to be P=246.73+/-0.49 d, a1 sin(i)=0.159+/-0.003 AU, M2 sin(i)=0.2062 (M1+M2)^(2/3)+/-0.0034 M_{\sun}. Assuming a primary mass of M1=0.08M_{\sun} (based on spectral type), we estimate the secondary minimum mass to be M2 sin(i)=0.054 M_{\sun}. With future photometric, spectroscopic, and interferometric observations it may be possible to determine the dynamical masses of both components directly, making this system one of the best characterized UCD binaries known.Comment: 11 pages, 2 figures. Accepted for publication in ApJ Letter

Finite precision measurement nullifies the Kochen-Specker theorem

Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden variable theories provided by Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-over-classical advantage for information processing can be derived from the Kochen-Specker theorem alone.Comment: 7 pages, plain TeX; minor corrections, interpretation clarified, references update

Observational constraints on the spectral index of the cosmological curvature perturbation

We evaluate the observational constraints on the spectral index $n$, in the context of the $\Lambda$CDM hypothesis which represents the simplest viable cosmology. We first take $n$ to be practically scale-independent. Ignoring reionization, we find at a nominal 2-$\sigma$ level $n\simeq 1.0 \pm 0.1$. If we make the more realisitic assumption that reionization occurs when a fraction $f\sim 10^{-5}$ to 1 of the matter has collapsed, the 2-$\sigma$ lower bound is unchanged while the 1-$\sigma$ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale-dependence of $n$, which occurs in a physically reasonable regime of parameter space.Comment: ReVTeX, 15 pages, 5 figures and 3 tables, uses epsf.sty Improved treatment of reionization and small bug fixed in the constant n case; more convenient parameterization and better treatment of the n dependence in the CMB anisotropy for the running mass case; conclusions basically unchanged; references adde

Further Evidence for Intrinsic Redshifts in Normal Spiral Galaxies

Evidence from galaxy absolute magnitudes, linear diameters, and HyperLeda images is presented which strongly supports the interpretation that some normal spiral galaxies can contain large non-cosmological (intrinsic) redshifts in excess of 5000 km s-1.Comment: 17 pages, Astrophysics&Space Science - Accepted for publicatio