The 4D SUSY algebra can be written as
{QAα,QB†β}=2mδABδαβ+2iZABΓ0αβ,
in a particular reference frame. One can find this formula in the Appendix B, page 448 of Polchinski's String Theory vol.II.
I am confused with the ′i′ before the central charge. If we do a Hermitian conjugate on both side:
{QA†α,QBβ}=2mδABδαβ−2iZAB(Γ0αβ)∗
and then exchange (A,α) with (B,β), the LHS is invariant. But the RHS is
2mδABδαβ−2iZBA(Γ0βα)∗=2mδABδαβ−2iZBA(Γ0)†αβ.
Since ZAB is anti-symmetric and (Γ0)†=−Γ0, It seems that we have the wrong sign before the central charge term:
2mδABδαβ−2iZAB(Γ0)αβ.
I think I made a mistake but I can not figure out where is it.
This post imported from StackExchange Physics at 2018-04-18 20:42 (UTC), posted by SE-user JQ Skywalker