Abstract
We reexamine the projective light cone limit of the gauge-invariant Green-Schwarz action on five-dimensional anti--de Sitter $\ensuremath{\bigotimes}$ the five-sphere. It implies the usual holography for ${\mathrm{AdS}}_{5},$ but also (a complex) one for ${\mathrm{S}}^{5}.$ The result is $N=4$ projective superspace, which unlike $N=4$ harmonic superspace can describe $N=4$ super Yang-Mills theory off shell.
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