, Volume 82, Issue 4, pp 545-606

Proof of confinement of static quarks in 3-dimensionalU(1) lattice gauge theory for all values of the coupling constant

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Abstract

We study the 3-dimensional pureU(1) lattice gauge theory with Villain action which is related to the 3-dimensional ℤ-ferromagnet by an exact duality transformation (and also to a Coulomb system). We show that its string tension α is nonzero for all values of the coupling constantg 2, and obeys a bound α≧const·m Dβ−1 for smallag 2, with β=4π2/g 2 and $m_D^2 = (2{\beta \mathord{\left/ {\vphantom {\beta a}} \right. \kern-0em} a}^3 )e^{ - \beta \upsilon _{Cb} {{(0)} \mathord{\left/ {\vphantom {{(0)} 2}} \right. \kern-0em} 2}} (a = lattice spacing)$ . A continuum limita→0,m D fixed, exists and represents a scalar free field theory of massm D. The string tension αm D −2 in physical units tends to ∞ in this limit. Characteristic differences in the behaviour of the model for large and small coupling constantag 2 are found. Renormalization group aspects are discussed.

Work supported in part by Deutsche Forschungsgemeinschaft
Communicated by R. Haag