I am considering spinors in a space-time which is R1,3×B being B a compact manifold of D dimensions.
I know that in ordinary 4 dimensional space-time spinors are representations of O(1,3). Now, in my case, are spinors expected to be reps of O(1,3+D)?
Does the compactness of B impose some restrictions to this? I have the feeling that we have to expect spinors to be reps of O(1,3)×O(D) since I don't feel that making a boost in the compact space is allowed but I am not sure.
Any clarification on the reps spinors are in in the mentioned space-time will be greatly appreciated.