Z(2) monopoles in lattice gauge theories

Halliday, I.G.; Schwimmer, A.

doi:10.1016/0370-2693(81)90630-4

Cited by 100 publications

(78 citation statements)

References 5 publications

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“…Note that λ α provides an analytic path between the weak coupling phase of Villain SO(3) and SU(2), since no phase transition except the above-mentioned monopole condensation transition has been found [30,31]. This is a strong argument in favour of the equivalence of the two theories in the continuum limit.…”

Section: Discussionmentioning

confidence: 91%

Comparison of SO(3) and SU(2) lattice gauge theory

2003

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The Villain form of SO(3) lattice gauge theory is studied and compared to Wilson's SU(2) theory. The topological invariants in SO(3) which correspond to twisted boundary conditions in SU(2) are discussed and lattice observables are introduced for them. An apparent SO(3) phase with negative adjoint Polyakov loop is explained in terms of these observables. The electric twist free energy, an order parameter for the confinement-deconfinement transition, is measured in both theories to calibrate the temperature. The results indicate that lattices with about 700 4 sites or larger will be needed to study the SO(3) confined phase. Alternative actions are discussed and an analytic path connecting SO(3) and SU(2) lattice gauge theory at weak coupling is exhibited. The relevance for confinement of the centre of the gauge group is discussed.

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Section: Discussionmentioning

confidence: 91%

Comparison of SO(3) and SU(2) lattice gauge theory

2003

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“…In 3+1 dimensions the theories exhibit in the β A -β F phase diagram bulk transitions [3,4] (see Fig. 1) related to the condensation of Z N magnetic monopoles σ c and electric vortices σ l [5,6].…”

Section: Introductionmentioning

confidence: 99%

Vortex topology and the continuum limit of lattice gauge theories

Burgio¹

2008

Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007)

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We study the stability of Z 2 topological vortex excitations in d+1 dimensional SU(2) Yang-Mills theory on the lattice at T = 0. This is found to depend on d and on the coupling considered. We discuss the connection with lattice artifacts causing bulk transitions in the β A -β F plane and draw some conclusions regarding the continuum limit of the theory.The XXV International Symposium on Lattice Field Theory

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“…From Eq. (14) we see that in the weak coupling limit 5 (ω → ∞) P adj → 1 3 . Again this agrees with the observations of Ref.…”

Section: The Nature Of the Phase Transitionmentioning

confidence: 70%

A study of the N=2 Kazakov-Migdal model

Gocksch¹

1993

Nuclear Physics B - Proceedings Supplements

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We study numerically the SU(2) Kazakov-Migdal model of 'induced QCD'. In contrast to our earlier work on the subject we have chosen here not to integrate out the gauge fields but to keep them in the Monte Carlo simulation. This allows us to measure observables associated with the gauge fields and thereby address the problem of the local Z 2 symmetry present in the model. We confirm our previous result that the model has a line of first order phase transitions terminating in a critical point. The adjoint plaquette has a clear discontinuity across the phase transition, whereas the plaquette in the fundamental representation is always zero in accordance with Elitzur's theorem. The density of small Z 2 monopoles shows very little variation and is always large. We also find that the model has extra local U(1) symmetries which do not exist in the case of the standard adjoint theory. As a result, we are able to show that two of the angles parameterizing the gauge field completely decouple from the theory and the continuum limit defined around the critical point can therefore not be 'QCD'.

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Z(2) monopoles in lattice gauge theories

Cited by 100 publications

References 5 publications

Comparison of SO(3) and SU(2) lattice gauge theory

Comparison of SO(3) and SU(2) lattice gauge theory

Vortex topology and the continuum limit of lattice gauge theories

A study of the N=2 Kazakov-Migdal model

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