Sigma-model formulation of Yang-Mills theory on a four-dimensional hypersphere: geodesics as paths
The sigma-model representation is constructed for Yang-Mills theory in the simplest conformally flat hyperspherical spaces SO(1,4)/SO(1,3), SO(2,3)/SO(1,3), and SO(5)/SO(4) (for the Euclidean variant). As in the case of Minkowski and Euclidean spaces, the Yang-Mills field is defined as b/sub ..mu../(x) = partial/sup y//sub ..mu../b(x,y)Vertical Bar/sub y/ = 0, where b(x,y) is a bilocal Goldstone field which takes on values in the algebra of the gauge group and is subject to certain covariant constraints. The minimal variant of these constraints leads to the string representation for b(x,y) in terms of the P-exponential along fixed paths coinciding with geodesics. As a result of the existence of closed geodesics on the hypersphere, contour functionals arise naturally in the theory, the contours being circles with the hypersphere radius. It is shown that the sigma-model representation is Weyl-covariant: its formulations in different conformally flat spaces are related by transformations of the coordinate y/sup rho/. The action of the conformal group on y/sup rho/ is found and the geometrical meaning of y/sup rho/ and the minimal constraints is explained.
- Research Organization:
- Joint Institute for Nuclear Research
- OSTI ID:
- 5595000
- Journal Information:
- Sov. J. Nucl. Phys. (Engl. Transl.); (United States), Vol. 37:2
- Country of Publication:
- United States
- Language:
- English
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