Integration of the $\mathrm{SL}(2,\mathbb R)/\mathrm{U}(1)$ Gauged WZNW Theory by Reduction and Quantum Parafermions

Using a gauge-invariant reduction, we directly integrate the $\mathrm{SL}(2,\mathbb R)/\mathrm{U}(1)$ WZNW theory. We prove that the conserved parafermions in this theory are coset currents. The parafermion algebra, the energy-momentum tensor, and “auxiliary” parafermions are quantized in a self-consistent manner.