Constraints on Higher Spin CFT2_2

We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with $\mathcal{W}_N$ symmetry in the "irrational" regime, where $c>N-1$ and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when $c>N-1$. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large $c$, this implies that the dual holographic theories of gravity in AdS$_3$, if they exist, have no local, perturbative degrees of freedom in the semi-classical limit.Comment: 31 pages+refs, 4 figure

Assessing Doppler velocities of Rankin Inlet F-region echoes

Doppler velocities observed by the Rankin Inlet (RKN) PolarDARN radar are assessed with a focus on data in the beams oriented roughly along the magnetic meridian. Hourly scatter plots for every month are built. They are shown to vary widely, with median values showing very clear magnetic local time variation with maximum magnitude during pre-noon and pre-midnight hours. The histograms contain a significant amount of very small velocity data that dominates at farther ranges and during the daytime. Near noon data show generally antisunward flows but at large ranges/magnetic latitudes and very close to noon, sunward flows occur for periods of positive IMF Bz. The reverse flows are stronger during spring equinox. The velocity magnitude was found to depend linearly on the IMF Bz and interplanetary electric field. Velocities are often found to be smaller than those expected from the statistical convection model of Ruohoniemi and Greenwald –1996