One-loop vacuum amplitude for D-branes in constant electromagnetic field

Following Polchinski's approach we calculate the one-loop vacuum amplitude for two parallel D-branes connected by open bosonic (neutral or charged)string in a constant uniform electromagnetic (EM) field. For neutral string, external EM field contribution appears as multiplier (Born-Infeld type action) of vacuum amplitude without external EM field. Hence,it gives the alternative way to see the inducing of Born-Infeld type action for description of D-branes. For charged string the situation is more complicated, it may indicate the necessity to modify the induced D-branes action in this case.