Gauge theories on sphere and Killing vectors

摘要

We provide a general method for studying 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. (C) 2003 Elsevier Inc. All rights reserved.