Deriving projective hyperspace from harmonic

Abstract

We derive actions for projective N=2 superspace ('hyperspace') from those for harmonic hyperspace, including that for non-Abelian Yang-Mills theory (a new result). The method uses Wick rotation of the sphere from complex conjugate coordinates to real, null ones, which can be treated as independent. The result can be considered 'holographic' in that the dimension of the internal (R symmetry) space is reduced from 2 to 1, by solving equations of motion or gauge conditions for dependence on the other coordinate. The auxiliary nature of the redundant dimension makes the hypergraph rules and evaluation almost identical.