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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:  $$ [\rho_{R}, [ \frac{1}{2\pi} \partial_x \phi_R^{(G)}},  e^{-i \phi_R^{(G)}}] \phi_R^{(G)}}} ]  = \delta(x-y) e^{-i\phi_R^{(G)}}(y)} $$