deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 9fbda4d..2d7b209 100644  --- a/untitled.tex  +++ b/untitled.tex 
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$$ -S_G = \frac{1}{4\pi K} \int d\tau dx \left[ i \partial_\tau \phi_R \partial_x \phi_R - i \partial_\tau \phi_L \partial_x \phi_L - ... \right]$$  It looks just like the perfect metal action, but he has (eq 2.22) $\psi_R \propto e^{i k_F x} e^{i \phi_R}, \psi_L \propto e^{-i k_F x} e^{i \phi_L}$. That means our chiral fields are off by a minus sign:  $$ \phi_I \equiv \phi^R_I  = - \phi_R^{(G))} $$ $$ \phi_{N+I} \equiv \phi^L_I  = - \phi_L^{(G))} $$ so finally I conclude that: