BPSM2-branes inAdS4×Q1,1,1and their dual loop operators

In this paper, we first compute the Killing spinors of ${\mathrm{AdS}}_{4}\ifmmode\times\else\texttimes\fi{}{Q}^{1,1,1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane solutions are found. The first class of solutions includes $M2$-branes dual to Wilson loops in the fundamental representation as a special case. The second class includes the candidates of the holographic description of vortex loops in the dual field theories.