# Is N=6 SUSY gravitino multiplet self-CPT?

I would like to understand why the $N=6$ gravitino (massless) multiplet $$\left(-\frac32,(-1)^{6},(-\frac12)^{15}, 0^{20}, (+\frac12)^{15}, +1^6, +\frac32 \right)$$

is not CPT self-conjuguate?. It seems to me that it must be self-conjiuguate but I did not find this statement in the litterature. My argument is that the Clifford vacuum form which it is contructed, $\lambda_0=-\frac32=-6/2+3/2$, is CPT self-conjuguate and the scalars $0^{20}$ belonging to real representation (isn't it?) of the automorphism group.

• Yes, it is self-conjugate, of course. Did you find any contrapositive statements in the literature, to the effect that this one breaks the general rule "maximum helicity"= N /4 implies self-conjugacy ? – Cosmas Zachos Nov 22 '17 at 14:53
• @CosmasZachos, thanks for your comment. No, I did not, in Wess & Bagger book they give, as examples, just the cases N=4,8. – Mohamed Vall Nov 22 '17 at 16:17
• So there probably isn't any, because it would not be sound, unless one cooked up a devilish bypass... – Cosmas Zachos Nov 22 '17 at 16:21
• Prof. @CosmasZachos, I am not sure that I understood your previous comment "breaks the general rule "maximum helicity"= N /4 implies self-conjugacy"; Is not N/4=3/2 for N=6 and so it satisfies this general rule? – Mohamed Vall Nov 22 '17 at 18:52
• Indeed, your multiplet satisfies the rule. AND there are NO contrapositive statements on it around, so, then, the rule must HOLD. I was just riffing on your expectation that if you don't find an obvious statement in the literature, it must be somehow under a cloud of suspicion. Thorough susy texts, of course, beat it to a tautology. – Cosmas Zachos Nov 22 '17 at 19:31