  N=2 quiver Chern-Simons theory has lately attracted attention as the world
volume theory of multiple M2 branes on a Calabi-Yau 4-fold. We study the
connection between the stringy derivation of M2 brane theories and the forward
algorithm which gives the toric Calabi-Yau 4-fold as the moduli space of the
quiver theory. Then the existence of the 3+1 dimensional parent, which is the
consistent 3+1 dimensional superconformal theory with the same quiver diagram,
is crucial for stringy derivation of M2 brane theories. We also investigate the
construction of M2 brane theories that do not have 3+1 dimensional parents. The
un-Higgsing procedure plays a key role to construct these M2 brane theories. We
find some N=2 quiver Chern-Simons theories which correspond to interesting
Calabi-Yau singularities.
