BFV-BRST quantization of two-dimensional supergravity

Abstract

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Radkin (BF) formalism, the anomaly-capceling 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 two-dimensional supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville &the gravity supermultiplets are introduced to make the BRST algebra close off-shell. Inchi~ion of them turns out to be essentially important especially in the super-light-cone gauge fixing, where the supercurvature equations (@g++ = 85x++ = 0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp(l,Z) current algebra symmetry in a transparent manner.PACS number(s): 11.25.Hf, 0485.+e, 11.25.Pm BFV-BRST QUANTIZATIdNOF TWO-DIMENSIONAL SUPERGRAVITY

Super-Virasoro Anomaly, Super-Weyl Anomaly, and the Super-Liouville Action for 2D Supergravity

“…The action S X + S g , however, is not invariant under the supersymmetry transformations modified to satisfy off-shell closure condition becuase of the super-Weyl anomaly. This can be remedied by introducing additional term to the action which is quadratic in the auxiliary field for the zweibein multiplet and turns out to be related with the cosmological term [1,27,23]. Thus the additional action including the cosmological term is given by…”

“…Since these gauges have already been taken up in ref. [23] for essentially the same action, we will be brief and contain them here to make the paper self-contained.…”

“…As was stressed in ref. [23], this is crucial in order to acheive quantization of the model for general gauge-fixings. The action S X + S g , however, is not invariant under the supersymmetry transformations modified to satisfy off-shell closure condition becuase of the super-Weyl anomaly.…”

“…In ref. [23] a slightly different gauge conditions, which are not manifestly invariant under the rigid Lorentz rotations on the two dimensional parameter space, are employed. Here we will adopt the Lorentz invariant guage conditions (6.10) to make it manifest the rigid Lorentz covariance of the ghost and gauge-fixing parts of the action.…”

“…Formulation of 2D (super)gravity as anomalous gauge theory has been argued in refs. [22,23], where the (super-)Weyl anomaly is canceled by introducing additional degrees of freedom identified with the (super-)Liouville mode.…”