A connection between ν-dimensional Yang-Mills theory and (ν−1)-dimensional,non-linear σ-models |
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Authors: | B Durhuus J Fröhlich |
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Institution: | 1. Institut des Hautes Etudes Scientifiques, F-91440, Bures-sur-Yvette, France
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Abstract: | We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ? v can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ? v?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 theU(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 couplingsg 2 ? 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. |
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