A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models

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Standard

A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models. / Durhuus, B.; Fröhlich, J.

I: Communications in Mathematical Physics, Bind 75, Nr. 2, 06.1980, s. 103-151.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Durhuus, B & Fröhlich, J 1980, 'A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models', Communications in Mathematical Physics, bind 75, nr. 2, s. 103-151. https://doi.org/10.1007/BF01222514

APA

Durhuus, B., & Fröhlich, J. (1980). A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models. Communications in Mathematical Physics, 75(2), 103-151. https://doi.org/10.1007/BF01222514

Vancouver

Durhuus B, Fröhlich J. A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models. Communications in Mathematical Physics. 1980 jun.;75(2):103-151. https://doi.org/10.1007/BF01222514

Author

Durhuus, B. ; Fröhlich, J. / A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models. I: Communications in Mathematical Physics. 1980 ; Bind 75, Nr. 2. s. 103-151.

Bibtex

@article{d8474d7590474925b35e0a64a9ecdd37,
title = "A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models",
abstract = "We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ℤv can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ℤv-1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for the U(n) ×U(n) σ-models, n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplings g2 ≳ O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2), U(n) or O(n), n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.",
author = "B. Durhuus and J. Fr{\"o}hlich",
year = "1980",
month = jun,
doi = "10.1007/BF01222514",
language = "English",
volume = "75",
pages = "103--151",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models

AU - Durhuus, B.

AU - Fröhlich, J.

PY - 1980/6

Y1 - 1980/6

N2 - We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ℤv can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ℤv-1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for the U(n) ×U(n) σ-models, n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplings g2 ≳ O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2), U(n) or O(n), n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.

AB - We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ℤv can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ℤv-1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for the U(n) ×U(n) σ-models, n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplings g2 ≳ O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2), U(n) or O(n), n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.

UR - http://www.scopus.com/inward/record.url?scp=34250249553&partnerID=8YFLogxK

U2 - 10.1007/BF01222514

DO - 10.1007/BF01222514

M3 - Journal article

AN - SCOPUS:34250249553

VL - 75

SP - 103

EP - 151

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -

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