Thursday, 27 November 2014

topological order - FQH Edge Theory as decoupled chiral bosons


The action describing the edge theory of the Fractional Quantum Hall effect is given by \begin{equation} S = \frac{1}{4\pi} \int \mathrm{d}x \ \mathrm{d}t \left[ K_{IJ} \ \partial_{t}\phi_{RI} \partial_{x}\phi_{RJ} - V_{IJ} \partial_{x}\phi_{RI}\partial_{x}\phi_{RJ} \right] \end{equation} for scalar fields $\phi_{RI}$ with $I=1....dim(K)$ and some symmetric,invertible matrix K and some positive definite, symmetric "velocity matrix" V.


The equations of motion for the fields read \begin{equation} \partial_{t}\partial_{x} K_{IJ}\phi_{RJ} - \partial_{x}^{2}V_{IJ}\phi_{RJ} = 0. \end{equation} This smells already a lot like the chiral boson theory in 1+1D Minkowski space which this action is supposed to be equivalent to. However I do not see the transformation that "decouples" the fields. Can anyone help?


Thanks in advance for your responses!




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