2
$\begingroup$

The only massless $N=8$ SUGRA multiplet is given by

$(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$

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?

$\endgroup$
1
$\begingroup$

Found the issue. The scalars in the N=8 gravity multiplet are real scalars, not complex. Same for the vector multiplet.

Thus the N=8 gravity multiplet can be decomposed as 1 copy of the N=4 gravity multiplet, 4 copies of the N=4 gravitino multiplet and 6 copies of the N=4 vector multiplet.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.