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In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1,1}$ and its certain orbifolds. Based on this, two classes of $M2$-branesolutions are found. The first class of solutions includes $M2$-branes dual toWilson loops in the fundamental representation as special cases. The secondclass includes the candidates of the holographic description of vortex loops inthe dual field theories.

BPS $M2$-branes in $AdS_4\times Q^{1, 1, 1}$ Dual to Loop Operators