DOI 10.1007/s100529900295
Analytic approach to confinement
and monopoles in lattice SU(2)
D. Gromes
Institut für Theoretische Physik der Universität
Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
(e-mail: d.gromes@thphys.uni-heidelberg.de)
Received: 27 August 1999 / Revised version: 29 October 1999 / Published online: 21 December 1999
Abstract
We extend the approach of Banks, Myerson, and Kogut
for the calculation of the Wilson loop in lattice U(1) to the
non-abelian SU(2) group. The original degrees of freedom of the
theory are integrated out, new degrees of freedom are introduced in
several steps. The centre group Z2 enters automatically through the
appearance of a field strength tensor
,
which takes on
the values 0 or 1 only. It obeys a linear field equation with the loop
current as source. This equation implies that
is non
vanishing on a two-dimensional surface bounded by the loop, and
possibly on closed surfaces. The two-dimensional surfaces have a
natural interpretation as strings moving in euclidean time.
In four dimensions we recover the dual Abrikosov string of
a type II superconductor, i.e. an electric string encircled by a
magnetic current. In contrast to other types of monopoles found in the
literature, the monopoles and the associated magnetic currents are
present in every configuration. With some plausible, though not
generally conclusive, arguments we are directly led to the area law
for large loops.
Copyright Springer-Verlag 2000
