The light-cone Hamiltonian approach is applied to the super D2-brane, and t
he equivalent area-preserving and U(1) gauge-invariant effective Lagrangian
, which is quadratic in the U(1) gauge field, is derived. The latter is rec
ognised to be that of the three-dimensional U(1) gauge theory, interacting
with matter supermultiplets, in a special external induced supergravity met
ric and the gravitino field, depending on matter fields. The duality betwee
n this theory and 11d supermembrane theory is demonstrated in the light-con
e gauge. (C) 1998 Published by Elsevier Science B.V. All rights reserved.