ANOMALY CANCELLATION IN THE PRESENCE OF A B-FIELD: THE PROJECTIVE CASE

Abstract

Using the modularity of the projective elliptic genera density introduced by Han and Mathai, we derive a new anomaly cancellation formula in the projective case, that is in the presence of a B-field, with flux that lifts to a torsion cohomology class. Then, using the twisted index theory developed by Mathai, Melrose and Singer, a setting is proposed to interpret this projective formula as the vanishing of an anomaly. This leads to new potential anomaly cancellations of anomalous fermions, such as the gravitino and the dilatino with "projective gauginos", existing even on non-spin manifolds.