Gravitational corrections to the Euler-Heisenberg Lagrangian
  We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic field nonperturbatively. The effective action is obtained in a form which generalizes the standard proper-time representation of the Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible applications. 
Fiorenzo Bastianelli, Jose Manuel Davila, Christian Schubert