Abstract
In this paper, we demonstrate that not only the heat kernel techniques are useful for computation of the parity anomaly, but also the parity anomaly turns out to be a powerful mean in studying the heat kernel. We show that the gravitational parity anomaly on four-dimensional manifolds with boundaries can be calculated using the general structure of the heat kernel coefficient [Formula: see text] for mixed boundary conditions, keeping all the weights of various geometric invariants as unknown numbers. The symmetry properties of the [Formula: see text]-invariant allow to fix all the relevant unknowns. As a byproduct of this calculation, we get an efficient and independent crosscheck (and confirmation) of the correction of the general structure of [Formula: see text] for mixed boundary conditions, previously suggested in [I. G. Moss, Anomalies, boundaries and the in–in formalism, J. Phys. A 45 (2012) 374022, https://doi.org/10.1088/1751-8113/45/37/374022 ].
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