arXiv subjects
Publications and source records attributed to M. Engelhardt.
A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The model quantitatively describes both confinement and the topological aspects of Yang-Mills theory. Details (including an adequate list of references) can be found in hep-lat/9912003 and hep-lat/0004013, both to appear in Nucl. Phys. B.
A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The random surfaces, governed by an action penalizing curvature, are investigated using Monte Carlo methods on a hypercubic lattice. A low-temperature confining phase and a high-temperature deconfined phase are generated by this simple dynamics. After fixing the parameters of the model such as to reproduce the relation between deconfinement temperature and zero-temperature string tension found in lattice Yang-Mills theory, a surprisingly accurate prediction of the spatial string tension in the deconfined phase results. Furthermore, the Pontryagin index associated with the lattice random surfaces of the model is constructed. This allows to also predict the topological susceptibility; the result is compatible with measurements in lattice Yang-Mills theory. Thus, for the first time an effective model description of the infrared sector emerges which simultaneously and consistently reproduces both confinement and the topological aspects of Yang-Mills theory within a unified framework. Further details can be found in hep-lat/9912003 and hep-lat/0004013, both to appear in Nucl. Phys. B.
A model for the infrared sector of Yang-Mills theory based on magnetic vortices represented by (closed) random surfaces is investigated using lattice Monte Carlo methods. The random surfaces are governed by a surface area action and a curvature action. The model generates a finite-temperature deconfinement transition; the coupling constants of the model can be chosen such as to reproduce the SU(2) Yang-Mills ratio of the deconfinement temperature to the square root of the zero-temperature string tension, T_c / sqrt{sigma_0} =0.69. This yields a physical trajectory in the space of coupling constants on which the confinement properties are approximately invariant. An at first sight surprisingly accurate prediction of the spatial string tension in the deconfined phase results, which can be made plausible in view of the specific space-time structure of the vortex configurations in this phase. The confinement properties are shown to be intimately tied to the percolation properties of the vortex surfaces.
The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed.
The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed.
We introduce quantum gauge fixing (QGF) as a new class of gauge fixings. While the maximal center gauge might not show vortex dominance, the confining properties of the vortices observed in past lattice calculations are argued to have been obtained in a gauge more akin to QGF than to the strict maximal center gauge.
In the framework of the center vortex picture of confinement, the nature of the deconfining phase transition is studied. Using recently developed techniques which allow to associate a center vortex configuration with any given lattice gauge configuration, it is demonstrated that the confining phase is a phase in which vortices percolate, whereas the deconfined phase is a phase in which vortices cease to percolate if one considers an appropriate slice of space-time.
The maximal center gauge, combined with center projection, is a means to associate Yang-Mills lattice gauge configurations with closed center vortex world-surfaces. This technique allows to study center vortex physics in lattice gauge experiments. In the present work, the continuum analogue of the maximal center gauge is constructed. This sheds new light on the meaning of the procedure on the lattice and leads to a sketch of an effective vortex theory in the continuum. Furthermore, the manner in which center vortex configurations generate the Pontryagin index is investigated. The Pontryagin index is built up from self-intersections of the vortex world-surfaces, where it is crucial that the surfaces be globally non-oriented.
By fixing lattice Yang-Mills configurations to the maximal center gauge and subsequently applying the technique of center projection, one can identify center vortices in these configurations. Recently, center vortices have been shown to determine the string tension between static quarks at finite temperatures (center dominance); also, they correctly reproduce the deconfining transition to a phase with vanishing string tension. After verifying center dominance also for the so-called spatial string tension, the present analysis focuses on the global topology of vortex networks. General arguments are given supporting the notion that the deconfinement transition in the center vortex picture takes the guise of a percolation transition. This transition is detected in Monte Carlo experiments by concentrating on various slices through the closed vortex surfaces; these slices, representing loops in lattice universes reduced by one dimension, clearly exhibit the expected transition from a percolating to a non-percolating, deconfined, phase. The latter phase contains a large proportion of vortex loops winding around the lattice in the Euclidean time direction. At the same time, an intuitive picture clarifying the persistence of the spatial string tension in the deconfined phase emerges.
Recent lattice calculations performed at zero temperature and in the maximal center gauge indicate that quark confinement can be understood in this gauge as due to fluctuations in the number of magnetic vortices piercing a given Wilson loop. This development has led to a revival of the vortex condensation theory of confinement. For a SU(2) gauge group, we show that also at finite temperatures, center vortices are the relevant collective infrared degrees of freedom determining the long-range static quark potential; in particular, their dynamics reflect the transition to the deconfining phase.
Center projection of SU(2) lattice gauge theory allows to isolate magnetic vortices as confining configurations. The vortex density scales according to the renormalization group, implying that the vortices are physical objects rather than lattice artifacts. Here, the binary correlations between points at which vortices pierce a given plane are investigated. We find an attractive interaction between the vortices. The correlations show the correct scaling behavior and are therefore physical. The range of the interaction is found to be (0.4 +/- 0.2) fm, which should be compared with the average planar vortex density of approximately 2 vortices/fm^2. We comment on the implications of these results for recent discussions of the Casimir scaling behavior of higher dimensional representation Wilson loops in the vortex confinement picture.