Bosonic Symmetries of $(2,0)$ DLCQ Field Theories

We investigate symmetries of the six-dimensional $(2,0)$ theory reduced along a compact null direction. The action for this theory was deduced by considering M-theory on $Ad{S}_7\times S^4$ and reducing the $Ad{S}_7$ factor along a time-like Hopf fibration which breaks one quarter of the supersymmetry and reduces the isometry group from $SO(6,2)$ to $SU(3,1)$. The boundary theory was previously shown to have 24 supercharges and a Lifshitz scaling symmetry. In this paper, we show that it has four boost-like symmetries and an additional conformal symmetry which furnish a representation of $SU(3,1)$ when combined with the other bosonic symmetries, providing a nontrivial check of the holographic correspondence.