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

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 adjo...

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Detalles Bibliográficos
Autores principales: de Forcrand, Philippe, Jahn, Oliver
Lenguaje:eng
Publicado: 2002
Materias:
Particle Physics - Lattice
Acceso en línea:https://dx.doi.org/10.1016/S0550-3213(02)01123-9
http://cds.cern.ch/record/589893
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author de Forcrand, Philippe
Jahn, Oliver
author_facet de Forcrand, Philippe
Jahn, Oliver
author_sort de Forcrand, Philippe
collection CERN
description 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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institution Organización Europea para la Investigación Nuclear
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spelling cern-5898932023-10-04T06:50:22Zdoi:10.1016/S0550-3213(02)01123-9http://cds.cern.ch/record/589893engde Forcrand, PhilippeJahn, OliverComparison of SO(3) and SU(2) lattice gauge theoryParticle Physics - LatticeThe 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.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.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.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.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.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.hep-lat/0211004CERN-TH-2002-312CERN-TH-2002-312oai:cds.cern.ch:5898932002-11-04
spellingShingle Particle Physics - Lattice
de Forcrand, Philippe
Jahn, Oliver
Comparison of SO(3) and SU(2) lattice gauge theory
title Comparison of SO(3) and SU(2) lattice gauge theory
title_full Comparison of SO(3) and SU(2) lattice gauge theory
title_fullStr Comparison of SO(3) and SU(2) lattice gauge theory
title_full_unstemmed Comparison of SO(3) and SU(2) lattice gauge theory
title_short Comparison of SO(3) and SU(2) lattice gauge theory
title_sort comparison of so(3) and su(2) lattice gauge theory
topic Particle Physics - Lattice
url https://dx.doi.org/10.1016/S0550-3213(02)01123-9
http://cds.cern.ch/record/589893
work_keys_str_mv AT deforcrandphilippe comparisonofso3andsu2latticegaugetheory
AT jahnoliver comparisonofso3andsu2latticegaugetheory

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