Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. II. Spin foam representation
arXiv:hep-th/0610237
Abstract
In this series of three papers, we generalize the derivation of dual photons and monopoles by Polyakov, and Banks, Myerson and Kogut, to obtain approximative models of SU(2) lattice gauge theory. Our approach is based on stationary phase approximations. In this second article, we start from the spin foam representation of 3-dimensional SU(2) lattice gauge theory. By extending an earlier work of Diakonov and Petrov, we approximate the expectation value of a Wilson loop by a path integral over a dual gluon field and monopole-like degrees of freedom. The action contains the tree-level Coulomb interaction and a nonlinear coupling between dual gluons, monopoles and current.
arXiv comment14 pages, 4 figures, 2 diagrams; shortened and relation between three articles clarified
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- A Dual Non-abelian Yang-Mills Amplitude in Four Dimensions
- Two-dimensional topological field theories coupled to four-dimensional BF theory
- A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework
- A Gauge-Independent Mechanism for Confinement and Mass Gap: Part II -- G=SU(2) and D=3
- Dual Non-Abelian Yang-Mills Simulations in Four Dimensions
- Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. I. BF Yang-Mills representation