High Energy Physics

Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of U(1) instantons for any instanton number. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally propose that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.

The axion provides a solution to the strong CP problem and is a cold dark matter candidate.  I'll briefly review the limits on the axion from particle physics, stellar evolution and cosmology.  The various constraints suggest that the axion mass is in the micro-eV to milli-eV range.  In this window, axions contribute significantly to the energy density of the universe in the form of cold dark matter.  It was recently found that dark matter axions thermalize and form a Bose-Einstein condensate (BEC).  As a result, it may be possible to distinguish axions from other forms of dark matter, such as weakly interacting massive particles (WIMPs), on observational grounds.  Axions accreting onto a galactic halo fall in with net overall rotation because almost all go to the lowest energy available state for given angular momentum.  In contrast, WIMPs accrete onto galactic halos with an irrotational velocity field.  The inner caustics are different in the two cases.  I'll argue that the dark matter is axions because there is observational evidence for the type of inner caustic produced by, and only by, an axion BEC.