Kac-Moody current algebras of D = 2 massless gauge theories,their representations and applications |
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| Institution: | 1. Department of Biological Sciences, Laboratory of Experimental Pathophysiology, Federal University of Ouro Preto, Minas Gerais, Brazil;2. Department of Biological Sciences, Laboratory of Immunobiology of Inflammation, Federal University of Ouro Preto, Minas Gerais, Brazil;3. Department of Biological Sciences, Laboratory of Biochemistry and Molecular Biology, Federal University of Ouro Preto, Minas Gerais, Brazil;4. Department of Biological Sciences, Laboratory of Biomaterials and Experimental Pathology, Federal University of Ouro Preto, Minas Gerais, Brazil;5. Department of Biological Sciences, Laboratory of Metabolic Biochemistry, Federal University of Ouro Preto, Minas Gerais, Brazil |
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| Abstract: | We give a classification of the Kac-Moody current algebras of all the possible massless fermion-gauge theories in two dimensions. It is shown that only Kac-Moody algebras based on AN, BN, CN, and DN in the Cartan classification with all possible central charge occur. The representation of local fermion fields and simply laced Kac-Moody algebras with minimal central charge in terms of free boson fields on a compactified space is discussed in detail, where stress is laid on the role played by the boundary conditions on the various collective modes. Fractional solitons and the possible soliton representation of certain nonsimply laced algebras is also analysed. We briefly discuss the relationship between the massless bound state sector of these two-dimensioned gauge theories and the critically coupled two-dimensional nonlinear sigma model, which share the same current algebra. Finally we briefly discuss the relevance of Sp(n) Kac-Moody algebras to the physics of monopole-fermion systems. |
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