Can Witten's Trick Apply to Any Number of Extra Dimensions?

[arivero]

I have remembered Witten had a trick to see massless particles in 4+n dimensions as if it were massive particles in 4 dimensions.

Does the trick works for any number of extra dimensions? Or only for 4+n=10?

 

[arivero]

I think the trick was in
"Search for a Realistic Kaluza-Klein Theory"
Edward Witten (Princeton U.) . PRINT-81-00
http://www.slac.stanford.edu/spires/find/hep/www?j=NUPHA,B186,412