Dynamics of SU(2) lattice gauge theories

Richard C. Brower; David A. Kessler; Herbert Levine

doi:10.1016/0550-3213(82)90467-9

Dynamics of SU(2) lattice gauge theories

Richard C. Brower, David A. Kessler, Herbert Levine

Research output: Contribution to journal › Article › peer-review

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Abstract

We study the dynamics of SU(2) lattice gaugee theories by concentrating on the underlying Z₂ structures of monopoles and vortices, adding a chemical potential for monopoles. The resulting abelian nature of these objects allows us to reliable computations for a wide range of couplings. In particular, by integrating over the non-abelian SO(3) degrees of freedom at strong coupling, an effective Z₂ theory emerges which at leading order is just the dual version of the Z₂-Higgs model. The phase boundaries are predicted to a few percent, as verified by Monte Carlo simulations. Our approach provides a framework for explaining and comparing many of the recently discovered features of the theory, including the Creutz crossover and the SO(3) phase transition. Also, we speculate on the relevance of these ideas for confinement and precocious scaling.

Original language	English
Pages (from-to)	77-106
Number of pages	30
Journal	Nuclear Physics B
Volume	205
Issue number	1
DOIs	https://doi.org/10.1016/0550-3213(82)90467-9
State	Published - 19 Apr 1982
Externally published	Yes

Bibliographical note

Funding Information:
* This research is supported in part by the National Science Foundation under grant no. PHY77-22864. 1 Permanent address: Department of Physics, University of California at Santa Cruz, Santa Cruz, CA 95064. 2 Permanent address: Theoretical Division, Los Alamos Scientific Laboratory, Los Alamos, NM 85744.

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title = "Dynamics of SU(2) lattice gauge theories",

abstract = "We study the dynamics of SU(2) lattice gaugee theories by concentrating on the underlying Z2 structures of monopoles and vortices, adding a chemical potential for monopoles. The resulting abelian nature of these objects allows us to reliable computations for a wide range of couplings. In particular, by integrating over the non-abelian SO(3) degrees of freedom at strong coupling, an effective Z2 theory emerges which at leading order is just the dual version of the Z2-Higgs model. The phase boundaries are predicted to a few percent, as verified by Monte Carlo simulations. Our approach provides a framework for explaining and comparing many of the recently discovered features of the theory, including the Creutz crossover and the SO(3) phase transition. Also, we speculate on the relevance of these ideas for confinement and precocious scaling.",

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N2 - We study the dynamics of SU(2) lattice gaugee theories by concentrating on the underlying Z2 structures of monopoles and vortices, adding a chemical potential for monopoles. The resulting abelian nature of these objects allows us to reliable computations for a wide range of couplings. In particular, by integrating over the non-abelian SO(3) degrees of freedom at strong coupling, an effective Z2 theory emerges which at leading order is just the dual version of the Z2-Higgs model. The phase boundaries are predicted to a few percent, as verified by Monte Carlo simulations. Our approach provides a framework for explaining and comparing many of the recently discovered features of the theory, including the Creutz crossover and the SO(3) phase transition. Also, we speculate on the relevance of these ideas for confinement and precocious scaling.

AB - We study the dynamics of SU(2) lattice gaugee theories by concentrating on the underlying Z2 structures of monopoles and vortices, adding a chemical potential for monopoles. The resulting abelian nature of these objects allows us to reliable computations for a wide range of couplings. In particular, by integrating over the non-abelian SO(3) degrees of freedom at strong coupling, an effective Z2 theory emerges which at leading order is just the dual version of the Z2-Higgs model. The phase boundaries are predicted to a few percent, as verified by Monte Carlo simulations. Our approach provides a framework for explaining and comparing many of the recently discovered features of the theory, including the Creutz crossover and the SO(3) phase transition. Also, we speculate on the relevance of these ideas for confinement and precocious scaling.

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Dynamics of SU(2) lattice gauge theories

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