On the quantisation and anomalies of antisymmetric tensor-spinors

TL;DR

This paper quantifies antisymmetric tensor-spinors using the BV formalism, revealing a new ghost in quadratic gauges and computing gravitational anomalies via the Atiyah-Singer index theorem.

Contribution

It introduces a BV-based quantisation method for fermionic p-forms and identifies a novel ghost contribution in quadratic gauges, advancing anomaly calculations.

Findings

Identification of a third ghost in quadratic gauges.

Application of the Atiyah-Singer index theorem to compute anomalies.

Extension of BV formalism to reducible gauge theories.

Abstract

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.