I am trying to understand what happens to the 32 supersymmetries of M-theory when it is compactified on $S^4$, with the other seven dimensions being flat, e.g., $\mathbb{R^7}$, $\mathbb{R^6} \times S^1$, or $\mathbb{R^5} \times S^1 \times S^1$. From what I have read, $S^4$ admits Killing spinors, so I believe some number of supersymmetries should be preserved in the 11-dimensional spacetime of M-theory. My question is, how many supersymmetries are actually preserved?

This post imported from StackExchange Physics at 2016-08-25 13:20 (UTC), posted by SE-user Meer Ashwinkumar