The only massless $N=8$ SUGRA multiplet is given by
where the greek upper indicies run from 1 to 8, which correspong from left to right as
- 1 graviton
- 8 gravitinos
- 28 vectors
- 56 fermions
- 70 scalars.
I want to decompose this multiplet into multiplets of massless N=4 SUGRA, which has the following multiplets
- Graviton multiplet; 1 graviton, 4 gravitinos, 6 vectors, 4 fermions, 1 scalar
- Gravitino multiplet; 1 gravitino, 4 vectors, 7 fermions, 4 scalars
- Vector multiplet; 1 vector, 4 fermions, 6 scalars.
The best I can do is try to write the N=8 Multiplet as (in terms of N=4 multiplets)
1 graviton multiplet + 4 gravitino multiplets + 6 vector multiplets.
but this still leaves me with 13 scalars left over. What am I doing wrong?