New insight into BRST anomalies in superstring theory

Abstract

Based on the extended BRST formalism of Batalin, Fradkin and Vilkovisky, we perform a general algebraic analysis of the BRST anomalies in superstring theory of Neveu-Schwarz-Ramond. Consistency conditions on the BRST anomalies are completely solved. The genuine super-Virasoro anomaly is identified with the essentially unique solution to the consistency condition without any reference to a particular gauge for the 2D supergravity fields. In a configuration space where metric and gravitino fields are properly constructed, general form of the super-Weyl anomaly is obtained from the super-Virasoro anomaly as its descendant. We give a novel local action of super-Liouville type, which plays a role of Wess-ZuminoWitten term shifting the super-Virasoro anomaly into the super-Weyl anomaly. These results reveal a hierarchial relationship in the BRST anomalies.

BFV-BRST quantization of two-dimensional supergravity

“…The construction of the action given here completely parallels that in the anomalous chiral gauge theories [18,28]. The resulting effective action contains two super-Liouville actions; One just coincides with the local but noncovariant counterterm found in [25], and acts as the Wess-Zumino-Witten term to shift the super-Virasoro anomaly to the super-Weyl anomaly. The other with the BF variables as super-Liouville fields cancels this super-Weyl anomaly.…”

“…The basic strategy parallels the bosonic string case. Our starting point is the most general form of the BRST anomalies in 2D SUGRA [25] in the extended phase space (EPS) of Batalin, Fradkin and Vilkovisky (BFV) [26]. The anomaly appeared there as anomalous Schwinger terms which destroy first-class nature of the super-Virasoro constraints.…”

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

“…(5.32) This is the local super-Liouville action with ξ, Λ identified with the super-Liouville fields and has been obtained in [21,23]. As discussed in [21,23] In this sense S g can be regarded as a WZW term converting the super-Virasoro anomaly into the super-Weyl anomaly. It can also be considered as a seagull term for the action (2.1) to maintain the covariance.…”

“…The variations of (2.7) under these transformations are computed to 21) where use has been made of the equations of motion for X and ψ ± . The local invariances of (2.1) thus lead to the equaitons of motion (2.13) and (2.14).…”

“…The connection between the (super-)Virasoro anomaly and the (super-)Weyl anomaly has been extensively studied in refs. [19,20,21]. Formulation of 2D (super)gravity as anomalous gauge theory has been argued in refs.…”