On the renormalization of the Polyakov loop

We discuss a non-perturbative renormalization of n-point Polyakov loop correlation functions by explicitly introducing a renormalization constant for the Polyakov loop operator on a lattice deduced from the short distance properties of 2-point correlators. We calculate this constant for the SU(3)gauge theory.Comment: 5 pages, 1 figure, To appear in the proceedings of Workshop on Strong and Electroweak Matter (SEWM 2002), Heidelberg, Germany, 2-5 Oct 200

Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and Ghost Propagators

We study the influence of Gribov copies on gluon and ghost propagators, evaluated numerically in pure SU(2) lattice gauge theory in the minimal Landau gauge. Simulations are done at four different values of $\beta$ (namely $\beta$ = 0, 0.8, 1.6 and 2.7) and for volumes up to $16^4$ (up to $24^4$ at $\beta$ = 1.6). For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy, even at very small values of the coupling $\beta$. On the contrary, for the ghost propagator, Gribov noise is clearly observable for the three values of $\beta$ in the strong-coupling regime. In particular, data corresponding to the minimal Landau gauge are always smaller than those obtained in a generic Landau gauge. This result can be qualitatively explained.Comment: 19 pages, including three figures; minor modifications following referee's suggestions. ZiF-MS-16/97 preprint. To appear in Nucl.Phys.

Critical behaviour and Scaling functions for the three-dimensional O(6) spin model with external field

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices. From Binder's cumulant at vanishing magnetic field we obtain the critical coupling J_c=1.42865(5) and verify this value with the \chi^2-method. The universal value of Binder's cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling we find the critical exponents \nu=0.818(5), \beta=0.425(2) and \gamma=1.604(6) from a finite size scaling analysis. We also determine the finite-size-scaling function on the critical line and the equation of state. Our O(6)-result for the equation of state is compared to the Ising, O(2) and O(4) results.Comment: 5 pages, 4 figures, To appear in the proceedings of Workshop on Strong and Electroweak Matter (SEWM 2002), Heidelberg, Germany, 2-5 Oct 200

The Nonabelian Screening Potential Beyond the Leading Order

The nonabelian screening potential is calculated in the temporal axial gauge. The Slavnov-Taylor identity is used to construct the three-gluon vertex function from the inverse gluon propagator. After solving the Schwinger - Dyson equation beyond leading order we find that the obtained momentum dependence of the gluon self-energy at high temperature does not correspond to an attractive QCD - Debye potential, but instead it is repulsive and power behaved ($\simeq 1/r^6$) at large distance.Comment: 10 pages, LATEX, ( 1 figure not included), BI-TP 94/0

D-Branes in Topological String Theory

This thesis is concerned with D-branes in topological string theory, focusing on the description of B-type D-branes in topological Landau-Ginzburg models. Such D-branes are characterized by matrix factorizations of the Landau-Ginzburg superpotential. After reviewing some aspects of topological string theory we give a detailed discussion of matrix factorizations. We discuss methods to calculate the effective superpotential in minimal models, putting emphasis on an algorithm to calculate the effective superpotential via deformations of matrix factorizations. We furthermore perform a non-trivial check of homological mirror symmetry for the torus.Comment: PhD thesis, 147+9 pages, 10 figure

A Gravity Theory on Noncommutative Spaces

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra a covariant tensor calculus is constructed and all the concepts like metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a theta-deformed Einstein-Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in theta.Comment: 28 pages, v2: coefficient in equ. (10.15) corrected, references added, v3: references added, published versio