# Tag Info

Hints: Tong is in eq. (4.26) calculating the OPE $${\cal R}[\partial X(z) :e^{ikX(w)}:]~=~\ldots\tag{4.26}$$ Note that the radial order ${\cal R}$ is implicitly written in Tong's text. He is using a nested Wick's theorem between radial order ${\cal R}$ and normal order $: :$, cf. e.g. my Phys.SE answer here. The contraction is $$C(z,w)~=~{\cal R}[ X(z) X(... 1 All the questions are basically answered in the classic paper "Supersymmetries and their representations". See also the wonderful talk: What's new with Q?. 1.- When the theory is conformal: In D=2 N=(1,0) (heterotic and type I strings), N=(1,1) (type IIB string), N=(2,0) (type IIA string), N=(2,2) ( N=2 strings), N=(2,1) (N=2 ... 1 The metrics, g_{ab} and \bar{g}_{ab} are conformally equivalent if we can write$$ \bar{g}_{ab} = \Omega^2g_{ab}\,,  where $\Omega\equiv \Omega(x)$ is a non-zero differentiable function of the space-time coordinates. In this case, their Weyl tensors are equivalent, i.e., $\bar{C}^{a}_{\,\,bcd} = {C}^{a}_{\,\,bcd}$. Setting $g_{ab}$ equal to the ...