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I'm reading Becker2Schwarz, chapter 5.1, about D0 branes in the GS formalism. They introduce kappa-symmetry, and end the section with "without this symmetry there would be the wrong number of propagating degrees of freedom".

I'm trying to understand that. The fermions [tex]\Theta^a[/tex] have, for D=10, [tex]2^5=32[/tex] complex components. But they are Majorana-Weyl, so this brings this number back to [tex]\frac{32}{4}=8[/tex] complex components. Kappa-symmetry implies that half of these fermions are gauge degrees of freedom, giving us 8 real components.

However, for the D0-brane, which is a particle, we start with 10 real components [tex]X^{\mu}[/tex]. Choosing e.g. the static gauge brings this back to 9 components. Obviously, to have as many bosonic degrees of freedom as fermionic (8 real), I need to get rid of another bosonic degree of freedom. How do I do that?

Perhaps I'm also confused by worldsheet SUSY versus target space SUSY; to realize target space SUSY on [tex]\{\Theta^a,X^{\mu}\}[/tex] one doesn't need this kappa symmetry, right?

Any help is appreciated :)