Light-cone quantization of the super-Liouville theory

Abstract

We quantise the super-Liouville equation using light-cone techniques. The theory is superconformally invariant at the quantum level, and c ̂ is a function of the coupling. When this coupling is tuned to certain rational numbers, c ̂ coincides with its values for the minimal series. We also obtain operator solutions for primary super-fields in the Neveu-Schwarz sector that provide explicit decompositions into monodromy invariant combinations of conformal blocks, and their conformal weights coincide with the known weights for primary fields in the minimal series. Certain terms present in the classical lagrangian are suppressed quantum mechanically as required by the correspondence with the super-Coulomb gas. This suppression also implies that the theory may be deformed into the exactly integrable supersymmetric sine-Gordon model by the addition to the lagrangian of a single primary field. This provides a lagrangian understanding of recent work by Zamolodchikov on the perturbation of the tricritical Ising model away from criticality.