Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime

We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection (that we call the electromagnetic field) is constant we compute the first two coefficients of the non-perturbative asymptotic expansion of the heat kernel which are of zero and the first order in Riemannian curvature and of arbitrary order in the electromagnetic field. We apply these results to the study of the effective action in non-perturbative electrodynamics in four dimensions and derive a generalization of the Schwinger's result for the creation of scalar and spinor particles in electromagnetic field induced by the gravitational field. We discover a new infrared divergence in the imaginary part of the effective action due to the gravitational corrections, which seems to be a new physical effect.