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arXiv · 2109.03963

On the quantisation and anomalies of antisymmetric tensor-spinors

Victor Lekeu·Yi Zhang
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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.

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Victor Lekeu, Yi Zhang. 2021-09-08. On the quantisation and anomalies of antisymmetric tensor-spinors. https://doi.org/10.1007/jhep11(2021)078

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