On the quantisation and anomalies of antisymmetric tensor-spinors

We perform the quantisation of antisymmetric tensor-spinors (fermionic $p$-forms) $\psi^\alpha_{\mu_1 \dots \mu_p}$ 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.