Z(3)-symmetric effective theory for pure gauge QCD at high temperature

We review the construction and basic properties of a three-dimensional effective field theory for high-temperature SU(3) Yang-Mills theory, which respects its center symmetry and was introduced in hep-ph/0604100. We explain why the phase diagram of the new theory is expected to closely resemble the one of the full theory and argue that this implies that it is applicable down to considerably lower temperatures than the usual non-Z(3)-symmetric 3d effective theory EQCD.Comment: 4 pages, 1 figure; to appear in the proceedings of Strong and Electroweak Matter 200

The QCD Equation of State - From Nuclear Physics to Perturbation Theory

In this talk, we briefly review the current understanding of the behavior of the QCD equation of state throughout the phase diagram. Special emphasis is given to regions of phenomenological interest, and a number of important open questions as well as directions of ongoing research are pointed out. These include in particular the region of low temperatures and (moderately) high densities, where at the moment we have extremely few first principles tools available.Comment: Invited talk at the workshop Excited QCD 2011, Lec Houches, Feb. 20-25, 2011. 6 pages, no figure

Scalar and Pseudoscalar Correlators in Yang-Mills Theory

Correlation functions of the FF and F\tilde{F} operators in hot SU(3) Yang-Mills theory have recently been studied both on the lattice and in perturbation theory, and the results subsequently compared to the strong coupling limit of large-N_c N=4 Super Yang-Mills theory, available through the AdS/CFT correspondence. Here, we review the perturbative calculations, covering both Euclidean spatial correlators and the UV limit of spectral densities, and comment on the emerging physical picture as well as on possible extensions of the present studies.Comment: 3 pages, 2 figures. To appear in the proceedings of The IX International Conference on Quark Confinement and the Hadron Spectrum, Madrid, Spain, 30 August - 3 September 201

Triangular ratio metric under quasiconformal mappings in sector domains

Hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result describes the behavior of the triangular ratio metric under quasiconformal maps from one sector onto another one.Comment: 14 pages, 1 figur