M-theory compactified on $S^4$

Question

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

Answer 1

This is answered in section 8.3 of

Paul de Medeiros, José Figueroa-O'Farrill, "Half-BPS M2-brane orbifolds", Adv. Theor. Math. Phys. Volume 16, Number 5 (2012), 1349-1408 (arXiv:1007.4761)

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