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This matches eqn 1.17 of Mike's notes under the identification $\phi_I \equiv \phi^R_I,\phi_{N+I} \equiv \phi^L_I$. Moreover, by using the above we can convince ourselves that:  $$ [\rho_{R}, e^{-i \phi_R^{(G)}}] =[ \frac{1}{2\pi} \partial_x \phi_R^{(G)}}, e^{-i \phi_R^{(G)}}} ] =  \delta(x-y) e^{-i\phi_R^{(G)}}(y)} $$ and for our chiral fields  $$ [\rho_{R,I}, e^{i \phi_I}] = [ \frac{-1}{2\pi} \partial_x \phi^R_I, e^{i \phi^R_I} ] = \delta(x-y) e^{i\phi^R_I(y)} $$