Question

How many Killing spinors exist on $S^5$?

Answer 1

killing spinours not exist because new tensors being used with scalar quantity of different theorems followed in thermodynamics of QFT theoroem

Answer 2

So, I know that on Sn, a spinor of the form

Σ±=1±iγαzα1+z2−−−−−√Σ0

where Σ0 is a constant spinor, is a Killing spinor on Sn because it satisfies

DaΣ±=±iγaΣ±

where Da is the covariant derivative (with the spin connection). But how many such Killing spinors exist?

I think the ± signs yield two linearly independent solutions. But for any sign choice, there ought to be 2D spinor components in SO(2D) and SO(2D+1). I am confused by the fact that the sphere is really a coset manifold:

Sn=SO(n+1)/SO(n).

How does one connect spinors of SO(n+1) and SO(n) to those of

Sn=SO(n+1)/SO(n)