  This talk is based on work made with L. Magnea and R. Russo. We give an
explicit expression of the multiloop partition function of open bosonic string
theory in the presence of a constant gauge field strength. The Schottky
parametrization allows to perform the field theory limit, which at two-loop
level reproduces the Euler-Heisenberg effective action for adjoint scalars
minimally coupled to the background gauge field.
