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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

[itex]\delta\phi=\epsilon\psi[/itex]

which implies in Majorana notation that

[itex]\delta a = \frac{1}{\sqrt{2}}\overline{\epsilon}\Psi[/itex]

[itex]\delta b = \frac{i}{\sqrt{2}}\overline{\epsilon}\gamma_{5} \Psi [/itex]

where [itex]\phi=(a+ib)/\sqrt{2}[/itex]