BFV-BRST Quantization of 2D Supergravity

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of 2D supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville and the gravity super-multiplets are introduced to make the BRST algebra close off-shell. Inclusion of them turns out to be essentially important especially in the super-lightcone gauge-fixing, where the super-curvature equations ( ∂ −g++ = ∂ 2 −χ++ = 0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the graded-SL(2,R) current algebra symmetry in a transparent manner. Permanent address: Faculty of Education, Niigata University, Niigata, 950-21, Japan.