  In the presence of a dilatonic coupling between an inflaton and a $U(1)$
gauge field, a persistent electric field (i.e., an anisotropic inflation) is
obtained as a solution of the classical field equations. We introduce charged,
massive, and conformally coupled fields into this model and study the pair
production of charged particles. The semiclassical approach allows us to
evaluate the induced current due to the pair production on the general
dilatonic factor and electric field. Solving the field equations with the
induced current, we find that the electric field shows a damped oscillation,
whose amplitude decays to zero regardless of the values of the masses of
charged fields. In other words, we derive a no-go theorem of anisotropic
inflation by taking into account the Schwinger mechanism.
