Superfield description of 10D SYM theory with magnetized extra dimensions

We present a four-dimensional (4D) N=1 superfield description of supersymmetric Yang-Mills (SYM) theory in ten-dimensional (10D) spacetime with certain magnetic fluxes in compactified extra dimensions preserving partial N=1 supersymmetry out of full N=4. We derive a 4D effective action in N=1 superspace directly from the 10D superfield action via dimensional reduction, and identify its dependence on dilaton and geometric moduli superfields. A concrete model for three generations of quark and lepton superfields are also shown. Our formulation would be useful for building various phenomenological models based on magnetized SYM theories or D-branes.