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High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
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.
