BFV-BRST QUANTIZATION OF 2-DIMENSION 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 s ystem. The BFV-BRST quantization applies to formulate the theory in th e most general class of gauges. A local effective action constructed i n the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of two-dime nsional supergravity fields, and the other contains the super-Liouvill e fields canceling the super-Weyl anomaly. Auxiliary fields for the Li ouville and the gravity supermultiplets are introduced to make the BRS T algebra close off-shell. Inclusion of them turns out to be essential ly important especially in the super-light-cone gauge fixing, where th e supercurvature equations (partial derivative(-g++)(3) = partial deri vative(-chi++)(2) = 0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp(1,2) current al gebra symmetry in a transparent manner.