On the quantisation and anomalies of antisymmetric tensor-spinors

Abstract

Abstract We perform the quantisation of antisymmetric tensor-spinors (fermionic p-forms) $$ {\psi}_{\mu_1\dots {\mu}_p}^{\alpha } $$ ψ μ 1 … μ p α 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.