Mass-Deformed Bagger-Lambert Theory and its BPS Objects

We find a sixteen supersymmetric mass-deformed Bagger-Lambert theory with $SO(4)\times SO(4)$ global R-symmetry. The R-charge plays the `non-central' term in the superalgebra. This theory has one symmetric vacuum and two in-equivalent broken sectors of vacua. Each sector of the broken symmetry has the SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric phase and any broken phase, and 1/4 BPS supertube-like objects, which may appear as anyonic q-balls in the symmetric phase or vortices in the broken phase. We also discuss mass deformations which reduces the number of supersymmetries.