Embedding of $F(4)$ in $OSp(8|4)$?

Question

Is the superconformal algebra in five dimensions, $F(4)$, a subalgebra of the (maximal) six-dimensional superconformal algebra $OSp(8|4)$?

Answer 1

So I asked Jeff Harvey about this, and this is what he told me.

"I suppose one could figure it out by first looking at whether there is an embedding of the bosonic subalgebra and if that works going on to look at the fermionic generators and checking if one can piece the two parts of the embedding together."

Answer 2

The bosonic subalgebra of $F(4)$ is $SO(5,2)\times SU(2)$. This certainly can be embedded into the bosonic subalgebra of $OSp(8|4)$ which is $SO(6,2)\times SO(5)$. The tricky bit is indeed to figure out the fermionic generators.

Answer 3

Apparently the answer to the question is "no", as shown in Appendix C.4.1 of this paper

https://arxiv.org/abs/0810.1484