Coupling of the BLG theory to a conformal supergravity background
  The Bagger-Lambert-Gustavsson theory is coupled to an off-shell D=3, N=8 conformal supergravity background. Local transformation laws of the conformal supergravity multiplet are obtained from those of the D=4, N=8 SO(8) gauged supergravity. The complete Lagrangian and local transformation laws of the coupled theory are obtained. As an application the supercurrent multiplet in a flat background is obtained. 
M. Nishimura and Y. Tanii
hep-th