  At strong-coupling and weak-field limit, the scalar Schwinger effect is
studied by the field-theoretical method of worldline instantons for dynamic
fields of single-pulse and sinusoidal types. By examining the Wilson loop along
the closed instanton path, corrections to the results obtained from
weak-coupling approximations are discovered. They show that this part of
contribution for production rate becomes dominant as Keldysh parameter
increases, it makes the consideration at strong coupling turn out to be
indispensable for dynamic fields. Moreover a breaking of weak-field condition
similar to constant field also happens around the critical field, defined as a
point of vacuum cascade. In order to make certain whether the vacuum cascade
occurs beyond the weak-field condition, following Semenoff and Zarembo's
proposal, the Schwinger effects of dynamic fields are studied with an
$\mathcal{N}=4$ supersymmetric Yang--Mills theory in the Coulomb phase. With
the help of the gauge/gravity duality, the vacuum decay rate is evaluated by
the string action with instanton worldline as boundary, which is located on a
probe D3-brane. The corresponding classical worldsheets are estimated by
perturbing the integrable case of a constant field.
