Abstract
We perform the quantisation of antisymmetric tensor-spinors (fermionic p-forms) \( {\psi}_{\mu_1\dots {\mu}_p}^{\alpha } \) 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.
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Lekeu, V., Zhang, Y. On the quantisation and anomalies of antisymmetric tensor-spinors. J. High Energ. Phys. 2021, 78 (2021). https://doi.org/10.1007/JHEP11(2021)078
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DOI: https://doi.org/10.1007/JHEP11(2021)078