I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without will of course remain in the NS sector.
I am wondering how to understand this phenomenon. What is the story for fermions? Their behavior under compactification is quite different, with the spinor bundle tending to split as a tensor product rather than as a direct sum.
This post imported from StackExchange Physics at 2016-03-03 18:47 (UTC), posted by SE-user Ryan Thorngren