Moduli and BPS configurations of the BLG theory

We study the moduli space of scalars in the BLG theory with and without a constant background four-form field. The classical vacuum moduli space is sixteen-dimensional in the absence of the four-form field. In its presence, however, the moduli space of BPS configurations may be reduced in dimension. We exemplify this with a BPS configuration having SO(1,2) world-volume symmetry and SO(4)×SO(4) R-symmetry in the presence of a four-form field, by constructing an explicit solution.