Field Theoretical Description of Quantum Hall Edge Reconstruction

We propose a generalization of the chiral Luttinger liquid theory to allow for a unified description of quantum Hall edges with or without edge reconstruction. Within this description edge reconstruction is found to be a quantum phase transition in the universality class of one-dimensional dilute Bose gas transition, whose critical behavior can be obtained exactly. At principal filling factors $\nu=1/m$, we show the additional edge modes due to edge reconstruction modifies the point contact tunneling exponent in the low energy limit, by a small and non-universal amount.