SUSY multiplets and CPT

1. Jul 17, 2012

302021895

When building the massless supermultiplets in N=1 supersymmetry one needs to add the CPT conjugate states to render the theory CPT invariant.

My question is, what do they mean by "CPT-conjugate"? Is it just the state with opposite helicity? Is it the state with opposite C, P and T? Or is it something else?

I wonder about this because when working with a massless chiral supermultiplet, it turns out that the real part of the complex scalar field is a real scalar field, but the imaginary part of the complex field is a real pseudoscalar field: the supersymmetry transformation in Weyl spinor notation is

$\delta\phi=\epsilon\psi$

which implies in Majorana notation that

$\delta a = \frac{1}{\sqrt{2}}\overline{\epsilon}\Psi$
$\delta b = \frac{i}{\sqrt{2}}\overline{\epsilon}\gamma_{5} \Psi$

where $\phi=(a+ib)/\sqrt{2}$