Maximal gauged Supegravity

Question

In a maximal gauged supergravity in five dimension, there is a maximal supersymmetry with local supersymmetry and as R-Symmetry there is a USp(8) group. The condition that supersymmetry is verified requires that, for example, the fermionic susy-shift vanishes. So that condition take the form :$D_{\mu}\epsilon^a=T^{ab}\gamma_{\mu}\epsilon_b$, where the covariant derivative is space-time covariant, the index $a,b$ are of USp(8)(fundamental repr), the $\epsilon$ are the Symplectic Majorana Spinor of susy variation and $T^{ab}$ is a tensor that contained the scalar of the theory. In the vacuum of theory, that is $AdS_5$ where all the scalar are set to zero, the tensor $T^{ab}$ is proportional to the identity matrix and the busy is maximal. Now i come to the point: if the $T^{ab}$ is not proportional to the identity but for example diagonal but with different entries, what does it mean that susy is not maximal? I mean, i agree this states but i don't understand how show it.

This post imported from StackExchange Physics at 2015-02-19 16:25 (UTC), posted by SE-user Andrea89

Comments

I don't understand what you are asking here. If you derived that the tensor is a multiple of the identity by using maximal SUSY, then it not being a multiple means that SUSY is not maximal.

This post imported from StackExchange Physics at 2015-02-19 16:25 (UTC), posted by SE-user ACuriousMind