Towards the Deconfinement Phase Transition in Hot Gauge Theories

The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. We discuss properties of chromoelectric and chromomagnetic sectors of the theory and show whereas electric charges carrying a unit of Z(N) charge are screened at high temperatures via dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local Z(N) symmetry in the magnetic sector. We argue this order parameter may be used to detect the deconfinement phase transition which is defined in terms of the screening mechanism.Comment: poster presented at LATTICE97; 3 pages, late

Tight bounds and conjectures for the isolation lemma

Given a hypergraph $H$ and a weight function $w: V \rightarrow \{1, \dots, M\}$ on its vertices, we say that $w$ is isolating if there is exactly one edge of minimum weight $w(e) = \sum_{i \in e} w(i)$. The Isolation Lemma is a combinatorial principle introduced in Mulmuley et. al (1987) which gives a lower bound on the number of isolating weight functions. Mulmuley used this as the basis of a parallel algorithm for finding perfect graph matchings. It has a number of other applications to parallel algorithms and to reductions of general search problems to unique search problems (in which there are one or zero solutions). The original bound given by Mulmuley et al. was recently improved by Ta-Shma (2015). In this paper, we show improved lower bounds on the number of isolating weight functions, and we conjecture that the extremal case is when $H$ consists of $n$ singleton edges. When $M \gg n$ our improved bound matches this extremal case asymptotically. We are able to show that this conjecture holds in a number of special cases: when $H$ is a linear hypergraph or is 1-degenerate, or when $M = 2$. We also show that it holds asymptotically when $M \gg n \gg 1$

Edge-coloring linear hypergraphs with medium-sized edges

Motivated by the Erd\H{o}s-Faber-Lov\'{a}sz (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper-edge sizes are bounded between $i$ and $C_{i,\epsilon} \sqrt{n}$ inclusive, then there is a list edge coloring using $(1 + \epsilon) \frac{n}{i - 1}$ colors. The dependence on $n$ in the upper bound is optimal (up to the value of $C_{i,\epsilon}$)

Deconfinement in QCD with dynamical quarks

We study the phase structure of full QCD within the canonical ensemble with respect to triality in a lattice formulation. The procedure for the calculation of the effective potentials in this case is given. As an example we consider the three dimensional SU(2) gauge model at finite temperatures in the strong coupling region. The potential exhibits a deconfinement phase transition unlike the similar potential obtained in the grand canonical ensemble which demonstrates explicit Z(N) symmetry breaking at any temperature. Furthermore, we investigate the effective potential with the chiral condensate included. In contradiction to other authors, we find chiral symmetry restoration in all triality sectors. In the scheme with massless staggered fermions we observe chiral symmetry restoration accompanying a deconfinement phase transition of first order. Above the critical point, besides two Z(2) symmetric "deconfining" vacua there exists a metastable "confining" vacuum in a wide region of parameters. Such a picture could be interpreted as an indication on a mixed state of hadrons and quarks in the vicinity of the critical line.Comment: 17 pages with 6 eps. figures include

Covariants of binary sextics and vector-valued Siegel modular forms of genus two

We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2

Fresh look on triality

Investigating the $Z_3$ symmetry in Quantum Chromodynamics (QCD) we show that full QCD with a vacuum of vanishing baryonic number does not lead to metastable phases. Rather in QCD with dynamical fermions, the degeneracy of $Z_3$ phases manifests itself in observables without open triality.Comment: 9 pages, 0 figures, latex, IK-TUW-Preprint 930840

Status of center dominance in various center gauges

We review arguments for center dominance in center gauges where vortex locations are correctly identified. We introduce an appealing interpretation of the maximal center gauge, discuss problems with Gribov copies, and a cure to the problems through the direct Laplacian center gauge. We study correlations between direct and indirect Laplacian center gauges.Comment: Presented by S. Olejnik at the NATO Advanced Research Workshop "Confinement, Topology, and other Non-Perturbative Aspects of QCD", Jan. 21-27, 2002, Stara Lesna, Slovakia. 10 pages, 3 figures (8 EPS files), uses crckapb.st