Abstract
A path integral formula is presented for the covariant gravitational anomaly of the self-dual anti-symmetric tensor gauge field. With the help of this formula, it is shown that the path integral Jacobian of the self-dual field strength under the general coordinate transformation is twice as large as the gravitational anomaly. It is also shown perturbatively that a chiral bi-spinor field accompanied with appropriate Faddeev-Popov ghosts describes a system of two self-dual anti-symmetric tensor gauge fields.
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