  Using the gauge-gravity duality, we study the holographic Schwinger effect by
performing the potential analysis on the confining D3- and D4-brane background
with D-instantons then evaluate the pair production/decay rate by taking
account into a fundamental string and a single flavor brane respectively. The
two confining backgrounds with D-instantons are obtained from the black
D(-1)-D3 and D0-D4 solution with a double Wick rotation. The total potential
and pair production/decay rate in the Schwinger effect are calculated
numerically by examining the NG action of a fundamental string and the DBI
action of a single flavor brane all in the presence of an electric field. In
both backgrounds our numerical calculation agrees with the critical electric
field evaluated from the DBI action and shows the potential barrier is
increased by the presence of the D-instantons, thus the production/decay rate
is suppressed by the D-instantons. Our interpretation is that particles in the
dual field theory could acquire an effective mass through the Chern-Simons
interaction or the theta term due to the presence of D-instantons so that the
pair production/decay rate in Schwinger effect is suppressed since it behaves
as $e^{-m^{2}}$. Our conclusion is in agreement with the previous results
obtained in the deconfined D(-1)-D3 background at zero temperature limit and
from the approach of the flavor brane in the D0-D4 background. In this sense,
this work may be also remarkable to study the phase transition in
Maxwell-Chern-Simons theory and observable effects by the theta angle in QCD.
