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

Z(3)-symmetric effective theory for SU(3) Yang-Mills theory at high temperature

A three-dimensional effective theory for high temperature SU(3) gauge theory, which maintains the Z(3) center symmetry of the full theory, is constructed. Such a Z(3) invariant effective theory should be applicable to a wider temperature range than the usual effective theory, known as EQCD, which fails to respect the center symmetry. This center-symmetric effective theory can reproduce domain wall and phase transition properties that are not accessible in EQCD. After identifying a convenient class of Z(3) invariant effective theories, we constrain the coefficients of the various terms in the Lagrangian using leading-order matching to EQCD at high temperature, plus matching of domain wall properties in the full theory. We sketch the expected structure of the phase diagram of the effective theory and briefly discuss the prospects of numerical simulations and the addition of quarks.Comment: 30 pages, 5 figures, v2 with minor correction

The N_f^3 g^6 term in the pressure of hot QCD

We determine the first independent part of the g^6 coefficient in the weak coupling expansion of the QCD pressure at high temperatures, the one proportional to the maximal power of the number of quark flavors N_f. In addition to introducing and developing computational methods that can be used in evaluating other parts of the expansion, our calculation provides a result that becomes dominant in the limit of large N_f and a fixed effective coupling g_{eff}^2 = g^2 N_f/2.Comment: 9 pages, 2 figures, revtex, v2: minor modifications and additional reference

Hyperfine Splitting and the Zeeman Effect in Holographic Heavy-Light Mesons

We inspect the mass spectrum of heavy-light mesons in deformed N=2 super Yang-Mills theory using the AdS/CFT correspondence. We demonstrate how some of the degeneracies of the supersymmetric meson spectrum can be removed upon breaking the supersymmetry, thus leading to the emergence of hyperfine structure. The explicit SUSY breaking scenarios we consider involve on one hand tilting one of the two fundamental D7 branes inside the internal R^6 space, and on the other hand applying an external magnetic field on the (untilted) branes. The latter scenario leads to the well-known Zeeman effect, which we inspect for both weak and strong magnetic fields.Comment: 5 pages, 1 figur

Pressure of the standard model

We review the computation of the thermodynamic pressure of the entire minimal standard model to three loop order, performed in hep-ph/0510375 and hep-ph/0512177.Comment: 4 pages, 3 figures, to appear in the proceedings of Strong and Electroweak Matter 200

Four-loop pressure of massless O(N) scalar field theory

Inspired by the corresponding problem in QCD, we determine the pressure of massless O(N) scalar field theory up to order g^6 in the weak-coupling expansion, where g^2 denotes the quartic coupling constant. This necessitates the computation of all 4-loop vacuum graphs at a finite temperature: by making use of methods developed by Arnold and Zhai at 3-loop level, we demonstrate that this task is manageable at least if one restricts to computing the logarithmic terms analytically, while handling the ``constant'' 4-loop contributions numerically. We also inspect the numerical convergence of the weak-coupling expansion after the inclusion of the new terms. Finally, we point out that while the present computation introduces strategies that should be helpful for the full 4-loop computation on the QCD-side, it also highlights the need to develop novel computational techniques, in order to be able to complete this formidable task in a systematic fashion.Comment: 34 page

Norm inequalities for vector functions

We study vector functions of ${\mathbb R}^n$ into itself, which are of the form $x \mapsto g(|x|)x\,,$ where $g : (0,\infty) \to (0,\infty)$ is a continuous function and call these radial functions. In the case when $g(t) = t^c$ for some $c \in {\mathbb R}\,,$ we find upper bounds for the distance of image points under such a radial function. Some of our results refine recent results of L. Maligranda and S. Dragomir. In particular, we study quasiconformal mappings of this simple type and obtain norm inequalities for such mappings.Comment: 19 page

Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence

The perturbative three-loop result for the thermodynamic potential of QCD at finite temperature and chemical potential as obtained in the framework of dimensional reduction is compared with the exact result in the limit of large flavor number. The apparent convergence of the former as well as possibilities for optimization are investigated. Corresponding optimized results for full QCD are given for the case of two massless quark flavors.Comment: REVTEX4, 4 pages, 3 color figures. v2: fig. 3 now includes also lattice data for two-flavor QCD at nonzero chemical potentia