Hard Thermal Loops and the Sphaleron Rate on the Lattice

We measure the sphaleron rate (topological susceptibility) of hot SU(2) gauge theory, using a lattice implementation of the hard thermal loop (HTL) effective action. The HTL degrees of freedom are implemented by an expansion in spherical harmonics and truncation. Our results for the sphaleron rate agree with the parametric prediction of Arnold, Son and Yaffe: Gamma ~ \alpha^5 T^4.Comment: 3 page

Chern-Simons Number Diffusion and Hard Thermal Loops on the Lattice

We develop a discrete lattice implementation of the hard thermal loop effective action by the method of added auxiliary fields. We use the resulting model to measure the sphaleron rate (topological susceptibility) of Yang-Mills theory at weak coupling. Our results give parametric behavior in accord with the arguments of Arnold, Son, and Yaffe, and are in quantitative agreement with the results of Moore, Hu, and Muller.Comment: 43 pages, 6 figure

Central extensions of current groups in two dimensions

In this paper we generalize some of these results for loop algebras and groups as well as for the Virasoro algebra to the two-dimensional case. We define and study a class of infinite dimensional complex Lie groups which are central extensions of the group of smooth maps from a two dimensional orientable surface without boundary to a simple complex Lie group G. These extensions naturally correspond to complex curves. The kernel of such an extension is the Jacobian of the curve. The study of the coadjoint action shows that its orbits are labelled by moduli of holomorphic principal G-bundles over the curve and can be described in the language of partial differential equations. In genus one it is also possible to describe the orbits as conjugacy classes of the twisted loop group, which leads to consideration of difference equations for holomorphic functions. This gives rise to a hope that the described groups should possess a counterpart of the rich representation theory that has been developed for loop groups. We also define a two-dimensional analogue of the Virasoro algebra associated with a complex curve. In genus one, a study of a complex analogue of Hill's operator yields a description of invariants of the coadjoint action of this Lie algebra. The answer turns out to be the same as in dimension one: the invariants coincide with those for the extended algebra of currents in sl(2).Comment: 17 page

Heavy quarkonium: progress, puzzles, and opportunities

A golden age for heavy quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the $B$-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations. The plethora of newly-found quarkonium-like states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c\bar{c}, b\bar{b}, and b\bar{c} bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.Comment: 182 pages, 112 figures. Editors: N. Brambilla, S. Eidelman, B. K. Heltsley, R. Vogt. Section Coordinators: G. T. Bodwin, E. Eichten, A. D. Frawley, A. B. Meyer, R. E. Mitchell, V. Papadimitriou, P. Petreczky, A. A. Petrov, P. Robbe, A. Vair

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin