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arXiv · hep-th/9502127

BFV-BRST Quantization of 2D Supergravity

T. Fujiwara·Y. Igarashi·R. Kuriki·T. Tabei
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Abstract

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 ($\dl^3_-g_{++} =\dl^2_-χ_{++}=0$) 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.

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T. Fujiwara, Y. Igarashi, R. Kuriki, T. Tabei. 1995-02-22. BFV-BRST Quantization of 2D Supergravity. https://doi.org/10.1103/physrevd.53.852

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