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A quick and simple question: one always talks about BPS states annihilating half the supercharges. What does that mean exactly?
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!
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!