On the quantisation and anomalies of antisymmetric tensor-spinors

Lekeu, Victor; Zhang, Yi

doi:10.1007/JHEP11(2021)078

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On the quantisation and anomalies of antisymmetric tensor-spinors

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Lekeu, Victor
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Zhang, Yi
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Lekeu, V., & Zhang, Y. (2021). On the quantisation and anomalies of antisymmetric tensor-spinors. Journal of High Energy Physics, 2021(11): 78. doi:10.1007/JHEP11(2021)078.

Cite as: https://hdl.handle.net/21.11116/0000-0009-2868-6

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.