Hypergeometric representation of a four-loop vacuum bubble

In this article, we present a new analytic result for a certain single-mass-scale four-loop vacuum (bubble) integral. We also discuss its systematic \e-expansion in d=4-2\e as well as d=3-2\e dimensions, the coefficients of which are expressible in terms of harmonic sums at infinity.Comment: 5 pages, to appear in the proceedings of the conference "Loops and Legs", Eisenach, 200

Four-Loop Decoupling Relations for the Strong Coupling

We compute the matching relation for the strong coupling constant within the framework of QCD up to four-loop order. This allows a consistent five-loop running (once the $\beta$ function is available to this order) taking into account threshold effects. As a side product we obtain the effective coupling of a Higgs boson to gluons with five-loop accuracy.Comment: 11 page

High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles

In this article we present a high-precision evaluation of the expansions in \e=(4-d)/2 of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of `QED-type' master integrals, i.e. those with a single mass scale only (i.e. $m_i\in\{0,m\}$) and an even number of massive lines at each vertex. Furthermore, we collect all that is known analytically about four-loop `QED-type' masters, as well as about {\em all} single-mass-scale vacuum integrals at one-, two- and three-loop order.Comment: 25 pages, uses axodraw.st

Completeness of Flat Coalgebraic Fixpoint Logics

Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular fixpoint logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL, and the logic of common knowledge. Extending this notion to the generic semantic framework of coalgebraic logic enables covering a wide range of logics beyond the standard mu-calculus including, e.g., flat fragments of the graded mu-calculus and the alternating-time mu-calculus (such as alternating-time temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We give a generic proof of completeness of the Kozen-Park axiomatization for such flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer Science, Springer, 2010, pp. 524-53

Nature and strength of bonding in a crystal of semiconducting nanotubes: van der Waals density functional calculations and analytical results

The dispersive interaction between nanotubes is investigated through ab initio theory calculations and in an analytical approximation. A van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92, 246401 (2004)] is used to determine and compare the binding of a pair of nanotubes as well as in a nanotube crystal. To analyze the interaction and determine the importance of morphology, we furthermore compare results of our ab initio calculations with a simple analytical result that we obtain for a pair of well-separated nanotubes. In contrast to traditional density functional theory calculations, the vdW-DF study predicts an intertube vdW bonding with a strength that is consistent with recent observations for the interlayer binding in graphitics. It also produce a nanotube wall-to-wall separation which is in very good agreement with experiments. Moreover, we find that the vdW-DF result for the nanotube-crystal binding energy can be approximated by a sum of nanotube-pair interactions when these are calculated in vdW-DF. This observation suggests a framework for an efficient implementation of quantum-physical modeling of the CNT bundling in more general nanotube bundles, including nanotube yarn and rope structures.Comment: 10 pages, 4 figure

Three-dimensional physics and the pressure of hot QCD

We update Monte Carlo simulations of the three-dimensional SU(3) + adjoint Higgs theory, by extrapolating carefully to the infinite volume and continuum limits, in order to estimate the contribution of the infrared modes to the pressure of hot QCD. The sum of infrared contributions beyond the known 4-loop order turns out to be a smooth function, of a reasonable magnitude and specific sign. Unfortunately, adding this function to the known 4-loop terms does not improve the match to four-dimensional lattice data, in spite of the fact that other quantities, such as correlation lengths, spatial string tension, or quark number susceptibilities, work well within the same setup. We outline possible ways to reduce the mismatch.Comment: 14 page

Understanding Confinement From Deconfinement

We use effective magnetic SU(N) pure gauge theory with cutoff M and fixed gauge coupling g_m to calculate non-perturbative magnetic properties of the deconfined phase of SU(N) Yang-Mills theory. We obtain the response to an external closed loop of electric current by reinterpreting and regulating the calculation of the one loop effective potential in Yang-Mills theory. This effective potential gives rise to a color magnetic charge density, the counterpart in the deconfined phase of color magnetic currents introduced in effective dual superconductor theories of the confined phase via magnetically charged Higgs fields. The resulting spatial Wilson loop has area law behavior. Using values of M and g_m determined in the confined phase, we find SU(3) spatial string tensions compatible with lattice simulations in the temperature interval 1.5T_c < T < 2.5T_c. Use of the effective theory to analyze experiments on heavy ion collisions will provide applications and further tests of these ideas.Comment: 18 pages, 5 figures, v2: fixed archive title (only

Automatic reduction of four-loop bubbles

We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from a practical viewpoint, for fully massive as well as QED-type integrals.Comment: 5 pages. Talk presented at RADCOR/Loops and Legs 2002, Kloster Banz, German