The following query is based on a reading of section 2.2 of a paper by Graña and Polchinski. The idea is to begin with the D3 brane action of the form
ds2=Z−1/2ημνdxμdxν+Z1/2dxmdxn
where μ,ν=0,1,2,3 and m,n=4,5,…,9 are indices along the longitudinal and transverse directions. Also, ημν=diag(−1,0,0,0) and Z is a harmonic function (in the paper it is taken as Z=R4/r4 where R4=4πgNα′2).
Now, type IIB superstring theory has two fermonic superpartners of the NS⊗NS and R⊗R fields, namely the dilatino and the gravitino, the supersymmetry transformations of which are given in terms of a spinor parameter ϵ in equations (2.1) and (2.2) of the paper. The authors further assert that for bosonic backgrounds, and for constant τ=C+ieΦ where C is the axion and Φ is the dilation, the dilatino variation is trivially zero. I understand this.
But when they set δψM=0 (M=0,1,…,9) they seem to go from
δψM=1κDMϵ+i480γM1…M5FM1…M5ϵ
to
kδψM=∂μϵ−18γμγw(1−Γ4)ϵ
where Γ4=iγ0123, wm=∂mlnZ and γw=γmwm.
I am not sure how they arrive at this equation. What happened to the i/480 term?
This post imported from StackExchange Physics at 2015-04-29 18:25 (UTC), posted by SE-user leastaction