Abstract
We present the generalization to spacetime dimension D=4n+2 of the Lorentz covariant quadratic lagrangian for pairs of (anti)self-dual fields previously obtained by the authors in D=2. In the process BRST quantizing this lagrangian a first-order quadratic lagrangian for ghost (anti)self-dual fields is found which, after gauge fixing, can be written in terms of bispinors and it turns out to be a Kähler-Dirac lagrangian. The coupling to gravity is straightforward and the gravitational anomaly due to (anti)self-dual fields is obtained directly from an action principle.
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