oint of the moduli space remains a current primary field after deformation of the kinetic term in the action. Thus one can consistently think of the current algebra primaries as the group element $g$ taken in the representation $\mathcal{R}$. It also implies that at the WZW points the current primaries are the affine primary fields.

As argued in section \[bootstrap\], we can compute the less singular terms in the current-primary OPE order by order in $f^2$, by using the current conservation and the Maurer-Cartan equation. Performing the calculation of higher order terms to order $f^2$, we find the OPE: $$\begin{aligned}
\label{jPhiO1}
j_{L,z}^a(z,\bar z) \phi(w,\bar w) = & \ - \frac{c_+}{c_+ + c_-} t^a \frac{\phi(w,\bar w)}{z-w} + :j^a_{L,z} \phi:(w,\bar w) \cr
& + {A^a}_c \log |z-w|^2 :j^c_{L,z}\phi:(w,\bar w) + {B^a}_c\frac{\bar z - \bar w}{z-w}:j^c_{L,\bar z}\phi:(w,\bar w) +... \cr
%
j_{L,\bar z}^a(z,\bar z) \phi(w,\bar w) = & \ - \frac{c_-}{c_+ + c_-} t^a \frac{\phi(w,\bar w)}{\bar z-\bar w} + :j^a_{L,\bar z} \phi:(w,\bar w) \cr
& - {A^a}_c \frac{z-w}{\bar z - \bar w} :j^c_{L,z}\phi: - {B^a}_c \log |z-w|^2 :j^c_{L,\bar z}\phi:(w,\bar w) +... \end{aligned}$$ where we dropped the subscript $\mathcal{R}$. The coefficients read: \[ABorder1\] [A\^a]{}\_c = i [f\^a]{}\_[cb]{} t\^b + (f\^4) ; \_c = i [f\^a]{}\_[cb]{} t\^b + (f\^4). The details of the calculation are given in appendix \[AppjPhi\]. Note that the coefficients of the simple poles are unmodified.

Current primaries are Virasoro primaries {#current-primaries-are-virasoro-primaries .unnumbered}
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We will now show that a primary field with respect to the left-current algebra is also a primary field with respect to the Virasoro algebra. The holomorphic worldsheet stress tensor is: T(z) = \_[ba]{}:j\^a\_[L,z]{} j\^b\_[L,z]{}:(z). Let us consider the OPE between a left-primary field $\phi$ and the holomorphic stress-tensor: $$\begin{aligned}
\phi(z) 2 c_1 T(w) &= \lim_{:x \to w:}\phi(z) j^a_{L,z}(x) j^b_{L,z}(w) \kappa