Comparison of Lattice Gauge Theories with Gauge Groups Z(2) and SU(2)

Mack, G.; Petkova, V.B.

doi:10.1016/0003-4916(79)90346-4

Comparison of Lattice Gauge Theories with Gauge Groups Z(2) and SU(2)

G. Mack
(
- Hamburg U.
)
,
V.B. Petkova
(
- Hamburg U.
)

Nov, 1978

39 pages

Published in:

Annals Phys. 123 (1979) 442

DOI:

10.1016/0003-4916(79)90346-4

Report number:

DESY-78-68

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Abstract: (Elsevier)

We study a model of a pure Yang Mills theory with gauge group SU (2) on a lattice in Euclidean space. We compare it with the model obtained by restricting variables to Z 2 . An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU (2) model whenever it holds for the corresponding Z 2 -model. The SU (2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the 't Hooft disorder parameter.

QUARK: CONFINEMENT
FIELD THEORETICAL MODEL: YANG-MILLS
GAUGE FIELD THEORY: Z(2)
GAUGE FIELD THEORY: SU(2)
GAUGE FIELD THEORY: EUCLIDEAN
APPROXIMATION: LATTICE
DUALITY: TRANSFORMATION
GAUGE FIELD THEORY: OSTERWALDER-SCHRADER POSITIVITY
GAUGE FIELD THEORY: CLUSTER EXPANSION
GAUGE FIELD THEORY: VORTEX

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