  We analyze electrostatic potentials in the holographic Schwinger effect. The
potential barrier for the pair production is estimated by a static potential
consisting of static mass energies, an electric potential from an external
electric-field, and the Coulomb potential between a particle and an
antiparticle. Given that the Coulomb potential is supposed to be evaluated by
the minimal surface attaching on the conformal boundary as usual, the critical
field, where the potential barrier vanishes, exhibits a deviation of 30% from
the one obtained from the Dirac-Born-Infeld (DBI) action. We reconsider this
issue by reexamining the Coulomb-potential part, which is evaluated by the
classical action of a string solution attaching on a probe D3-brane sitting at
an intermediate position in the bulk AdS. Then the resulting critical-field
completely agrees with the DBI result. This agreement gives rise to a strong
support for the holographic scenario. We also discuss the finite-temperature
case and the temperature-dependent critical-field also agrees with the DBI
result.
