BFV-BRST Quantization of 2D Supergravity

TL;DR

This paper develops a BRST quantization framework for 2D supergravity using BFV formalism, introducing super-Liouville fields to cancel anomalies and revealing underlying symmetries.

Contribution

It presents a novel application of BFV-BRST quantization to 2D supergravity, incorporating super-Liouville fields and auxiliary fields for off-shell closure and gauge fixing.

Findings

Constructed a local effective action with super-Liouville fields.

Derived super-curvature equations in super-lightcone gauge.

Clarified the origin of graded-SL(2,R) symmetry.

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 ($\dl^3_-g_{++} =\dl^2_-\chi_{++}=0$) 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.