  We present the multiloop partition function of open bosonic string theory in
the presence of a constant gauge field strength, and discuss its low-energy
limit. The result is written in terms of twisted determinants and differentials
on higher-genus Riemann surfaces, for which we provide an explicit
representation in the Schottky parametrization. In the field theory limit, we
recover from the string formula the two-loop Euler-Heisenberg effective action
for adjoint scalars minimally coupled to the background gauge field.
