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Gauge theories on sphere and Killing vectors. (English) Zbl 1045.81043

Summary: We provide a general method for studying a manifestly O(\(n+1\)) covariant formulation of \(p\)-form gauge theories by stereographically projecting these theories, defined in flat Euclidean space, onto the surface of a hypersphere. The gauge fields in the two descriptions are mapped by conformal Killing vectors while conformal Killing spinors are necessary for the matter fields, allowing for a very transparent analysis and compact presentation of results. General expressions for these Killing vectors and spinors are given. The familiar results for a vector gauge theory are reproduced.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
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