QCD thermodynamics at zero and non-zero density

We present recent results on thermodynamics of QCD with almost physical light quark masses and a physical strange quark mass value. These calculations have been performed with an improved staggerd action especially designed for finite temperature lattice QCD. In detail we present a calculation of the transition temperature, using a combined chiral and continuum extrapolation. Furthermore we present preliminary results on the interaction measure and energy density at almost realistic quark masses. Finally we disscuss the response of the pressure to a finite quark chemical potential. Within the Taylor expansion formalism we calculate quark number susceptibilities and leading order corrections to finite chemical potential. This is particularly usefull for mapping out the critical region in the QCD phase diagram.Comment: Invited talk at 3rd International Workshop on Critical Point and Onset of Deconfinement, Florence, Italy, 3-6 Jul 200

Lattice QCD at Finite Density

I discuss different approaches to finite density lattice QCD. In particular, I focus on the structure of the phase diagram and discuss attempts to determine the location of the critical end-point. Recent results on the transiton line as function of the chemical potential ($T_c(\mu_q)$) are reviewed. Along the transition line, hadronic fluctuations have been calculated, which can be used to characterize properties of the Quark Gluon plasma and eventually can also help to identify the location of the critical end-point in the QCD phase diagram on the lattice and in heavy ion experiments. Furthermore, I comment on the structure of the phase diagram at large $\mu_q$.Comment: Plenary talk at XXIVth International Symposium on Lattice Field Theory (Lattice 2006). Version to appear as PoS (LAT2006) 021; references adde

The Non-Abelian Self-Dual String and the (2,0)-Theory

We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the corresponding equations of motion and discuss their properties. The underlying geometric picture is a string structure, i.e. a categorified principal bundle with connection whose structure 2-group is the string 2-group. We readily write down the explicit elementary solution to our equations, which is the categorified analogue of the 't Hooft-Polyakov monopole. Our solution passes all the relevant consistency checks; in particular, it is globally defined on $\mathbb{R}^4$ and approaches the abelian self-dual string of charge one at infinity. We note that our equations also arise as the BPS equations in a recently proposed six-dimensional superconformal field theory and we show that with our choice of higher gauge structure, the action of this theory can be reduced to four-dimensional supersymmetric Yang-Mills theory.Comment: v3: 1+42 pages, presentation improved, typos fixed, published versio

Chiral perturbation theory for lattice QCD with a twisted mass term

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term for two degenerate quark flavours is considered in the framework of chiral perturbation theory. The pion mass and decay constant are calculated in next-to-leading order including terms linear in the lattice spacing $a$.Comment: 5 pages, LaTeX2e, typos corrected, 2 references adde

Towards an M5-Brane Model I: A 6d Superconformal Field Theory

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the ABJM model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2,0)-theory.Comment: 1+39 pages, v3: minor improvements, published versio

Efficient Management of Short-Lived Data

Motivated by the increasing prominence of loosely-coupled systems, such as mobile and sensor networks, which are characterised by intermittent connectivity and volatile data, we study the tagging of data with so-called expiration times. More specifically, when data are inserted into a database, they may be tagged with time values indicating when they expire, i.e., when they are regarded as stale or invalid and thus are no longer considered part of the database. In a number of applications, expiration times are known and can be assigned at insertion time. We present data structures and algorithms for online management of data tagged with expiration times. The algorithms are based on fully functional, persistent treaps, which are a combination of binary search trees with respect to a primary attribute and heaps with respect to a secondary attribute. The primary attribute implements primary keys, and the secondary attribute stores expiration times in a minimum heap, thus keeping a priority queue of tuples to expire. A detailed and comprehensive experimental study demonstrates the well-behavedness and scalability of the approach as well as its efficiency with respect to a number of competitors.Comment: switched to TimeCenter latex styl