Abstract
We perform the quantisation of antisymmetric tensor-spinors (fermionic p-forms) {psi}_{mu_1dots {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.
Highlights
Our motivation for examining these fields is twofold
We put a special emphasis on quadratic gauges containing a differential operator: there, a third propagating ghost appears, as was first described within this formalism in a manifestly local way by Batalin and Kallosh in [21]
We discuss in the BV formalism the appearance of the ‘third ghost’ for quadratic gauges in an arbitrary gauge theory
Summary
We begin with a short review of BV quantisation of irreducible gauge theories and apply it to the free gravitino field.
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