  We study primordial electromagnetic fields in effective actions of string
theory. In contrast to a conventional scenario of producing primordial
electromagnetic fields induced by the axion inflation, we deal with the
Dirac-Born-Infeld action as a non-linear generation of Maxwell theory. It turns
out that the intensity of generated electromagnetic fields is bounded from
above by the string scale which can also be rewritten in terms of supersymmetry
breaking scale in the context of type IIB Large Volume Scenario. The
instability parameter $\xi$ is constrained by the tadpole cancellation
condition of D3-branes and a realization of hierarchy between the string scale
and the Hubble scale of inflation. Hence, the magnetogenesis can be realized in
the limited corner of the string landscape due to the ${\cal O}(1)$ value of
the coefficient of Chern-Simons coupling.
