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nrqed

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A quote from the paper "Into the amplituhedron"

"The amplituhedron ##A_{n,k,L}## for n particle ##N^k MHV## amplitudes at L loops lives in G(k,k+4;L) which is the space of k- planes Y in k+4 dimensions... "

I am trying to understand the meaning of the "4" here. Later they introduce the twistors Z and they say that there are n such twistors, each of dimension k+4. There is one twistor per particle, but why does each twistor have k+4 components? 4 I would understand (they probably have in mind spin 1/2 particles so there are four components for the helicity spinors), but why would the fact that we have the ##N^k## MHV increase the number of components of each particle's spinor?

Thanks in advance.