Gauge Theories on Sphere and Killing Vectors

Abstract

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.

19 pages, LaTex errors fixed; marginal changes, To appear in Annals of Physics

References in corpus (2)

• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Antisymmetric Tensor Gauge Fields on S_4

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