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nrqed

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For example, in a pedagogical article by Alvarez-Gaumé and Hassan they give the anticommutator of one set of supercharges to be

[itex] \{b_\alpha, b_\beta^\dagger \} = \delta_{\alpha \beta} (M-\sqrt{2} Z) [/itex]

They also give anti commutation relations for other modes which are not annihilated by BPS states.

They then say that from this it is obvious that BPS states (with [itex] M = \sqrt{2} Z[/itex]) annihilate half the suzy generators.

What does this mean, exactly? The above relation implies that on a BPS state, [itex] b_\alpha b_\beta^\dagger - b_\beta^\dagger b_\alpha [/itex] gives zero, but how does that lead to the state annihilating half the generators? I could imagine that maybe given that a BPS state is a state of lowest energy in a given sector we possibly impose that the annihilation operators [itex] b_\alpha [/itex] may be annihilating the states. But that still would not imply that a creation operator applied on the BPS state will give zero.

I know this is a trivial question and probably just a question of terminology but I would appreciate it if someone could clear that up for me.

Thanks!