On the quantisation and anomalies of antisymmetric tensor-spinors

We perform the quantisation of antisymmetric tensor-spinors (fermionic $p$-forms) ${\psi }_{{\mu }_1\dots {\mu }_p}^{\alpha }$ using the Batalin-Vilkovisky field-antifield formalism. Just as for the gravitino ($p=1$), an extra propagating Nielsen-Kallosh ghost appears in quadratic gauges containing a differential operator. The appearance of this `third ghost’ is described within the BV formalism for arbitrary reducible gauge theories. We then use the resulting spectrum of ghosts and the Atiyah-Singer index theorem to compute gravitational anomalies.