Strong coupling expansion for Yang-Mills theory at finite temperature

Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for $\beta<\beta_c$, where $\beta_c$ denotes the nearest singularity of the free energy on the real axis. The accessible temperature range is thus the confined regime up to the deconfinement transition. We have calculated the first few orders of these expansions of the free energy density as well as the screening masses for the gauge groups SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball gas of the lowest mass glueballs up to the calculated order. Our result can be used to fix the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method, and shows from first principles that in the confined phase this constant is indeed exponentially small. Similarly, our results also explain the weak temperature dependence of glueball screening masses below $T_c$, as observed in Monte Carlo simulations. Possibilities and difficulties in extracting $\beta_c$ from the series are discussed.Comment: 7 pages, 3 figures, 1 tables, corrected typo

Witten index and phase diagram of compactified N=1 supersymmetric Yang-Mills theory on the lattice

Owing to confinement, the fundamental particles of N=1 Supersymmetric Yang-Mills (SYM) theory, gluons and gluinos, appear only in colourless bound states at zero temperature. Compactifying the Euclidean time dimension with periodic boundary conditions for fermions preserves supersymmetry, and confinement is predicted to persist independently of the length of the compactified dimension. This scenario can be tested non-perturbatively with Monte-Carlo simulations on a lattice. SUSY is, however, broken on the lattice and can be recovered only in the continuum limit. The partition function of compactified N=1 SYM theory with periodic fermion boundary conditions corresponds to the Witten index. Therefore it can be used to test whether supersymmetry is realized on the lattice. Results of our recent numerical simulations are presented, supporting the disappearance of the deconfinement transition in the supersymmetric limit and the restoration of SUSY at low energies.Comment: 7 pages, 3 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japa

Twisted mass lattice QCD with non-degenerate quark masses

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term is considered in the framework of chiral perturbation theory. For two and three numbers of quark flavours, respectively, with non-degenerate quark masses the pseudoscalar meson masses and decay constants are calculated in next-to-leading order including lattice effects quadratic in the lattice spacing a.Comment: 9 pages, LaTeX2e, reference adde

Phase structure of the N=1 supersymmetric Yang-Mills theory at finite temperature

Supersymmetry (SUSY) has been proposed to be a central concept for the physics beyond the standard model and for a description of the strong interactions in the context of the AdS/CFT correspondence. A deeper understanding of these developments requires the knowledge of the properties of supersymmetric models at finite temperatures. We present a Monte Carlo investigation of the finite temperature phase diagram of the N=1 supersymmetric Yang-Mills theory (SYM) regularised on a space-time lattice. The model is in many aspects similar to QCD: quark confinement and fermion condensation occur in the low temperature regime of both theories. A comparison to QCD is therefore possible. The simulations show that for N=1 SYM the deconfinement temperature has a mild dependence on the fermion mass. The analysis of the chiral condensate susceptibility supports the possibility that chiral symmetry is restored near the deconfinement phase transition.Comment: 26 pages, 12 figure

Twisted mass chiral perturbation theory for 2+1+1 quark flavours

We present results for the masses of pseudoscalar mesons in twisted mass lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate doublet of s and c quarks in the framework of next-to-leading order chiral perturbation theory, including lattice effects up to O(a^2). The masses depend on the two twist angles for the light and heavy sectors. For maximal twist in both sectors, O(a)-improvement is explicitly exhibited. The mixing of flavour-neutral mesons is also discussed, and results in the literature for the case of degenerate s and c quarks are corrected.Comment: LaTeX2e, 12 pages, corrected typo

Interdisciplinary Monte Carlo Simulations

Biological, linguistic, sociological and economical applications of statistical physics are reviewed here. They have been made on a variety of computers over a dozen years, not only at the NIC computers. A longer description can be found in our new book, an emphasis on teaching in Eur.J.Phys. 26, S 79 and AIP Conf. Proc. 779, 49, 56, 69 and 75.Comment: 11 pages including many Figs.; for 3rd NIC Symposium, Julich, 3/0