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N=2 quiver Chern-Simons theory has lately attracted attention as the worldvolume theory of multiple M2 branes on a Calabi-Yau 4-fold. We study theconnection between the stringy derivation of M2 brane theories and the forwardalgorithm which gives the toric Calabi-Yau 4-fold as the moduli space of thequiver theory. Then the existence of the 3+1 dimensional parent, which is theconsistent 3+1 dimensional superconformal theory with the same quiver diagram,is crucial for stringy derivation of M2 brane theories. We also investigate theconstruction of M2 brane theories that do not have 3+1 dimensional parents. Theun-Higgsing procedure plays a key role to construct these M2 brane theories. Wefind some N=2 quiver Chern-Simons theories which correspond to interestingCalabi-Yau singularities.

M2-branes Theories without 3+1 Dimensional Parents via Un-Higgsing