Supersymmetric Casimir energy on N=1 superconformal field theories
ABSTRACT
The evaluation of the Casimir energy from first principles on N=1 superconformal field theories is provided. First a comprehensive introduction on gauge anomalies in a unified form will be given by highlighting on the superconformal anomalies and Ward Identities applying the gauging procedure of the superconformal group. Moreover, after reviewing the three definitions of Casimir energy on conformal field theories, a careful derivation of the supersymmetric Casimir energy on a general superconformal background is described by constructing the background supercharge algebra taking into account the anomalous supercurrent transformations. Ward identities imply the existence of one parameter families of generalized conserved currents associated with a background Killing vector, which interpolate between the consistent and the covariant R-current and energy momentum tensor. As an illustrative example the resulting Casimir energy on the squashed sphere is presented. Interestingly enough, the resulting Casimir energy differs from the known results in bibliography. The source of this discrepancy is emphasized, based on the scheme dependence of holomorphy of the effective action on the background geometry parameters. Conclusions include the on going work on anomalous N=1 superconformal Wess-Zumino actions and couterterms relating different anomaly schemes towards completing this puzzle.