Abstract
We review the quantum status of the non-linear bosonic δ-models built on compact homogeneous spaces. The subclass of Kähler manifolds can be parametrized in such a way that multiplicative renormalizability holds, to all-order of perturbation theory. The essential ingredients are the homogeneity of the space and the existence of a charge Y that separates the fields in ϕ and ϕ : for these Kähler manifolds, a family of coordinate frames exists such that the non-linear isometries are holomorphic. The method is exemplified on the special case SU(3)/(U(l)xU(l)).
The material Uresented here results from work done in Paris with François DEL DUC and Galliano VALENT.
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Bonneau, G. (1988). Renormalization of bosonic non-linear δ-models built on compact homogeneous manifolds. In: Breitenlohner, P., Maison, D., Sibold, K. (eds) Renormalization of Quantum Field Theories with Non-linear Field Transformations. Lecture Notes in Physics, vol 303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033722
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DOI: https://doi.org/10.1007/BFb0033722
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