M5-branes in ${\mathrm{AdS}}_4\times Q^{1,1,1}$ spacetime

In this paper, we study the M5-brane configurations in ${\mathrm{AdS}}_4\times Q^{1,1,1}$ spacetime. We consider the configurations with an ${\mathrm{AdS}}_2$ factor embedding into ${\mathrm{AdS}}_4$ and manage to construct two solutions, which could be dual to line defects in the boundary gauge theory. Moreover, we discuss their Bogomol’nyi-Prasad-Sommerfield (BPS) nature and find that neither of them is supersymmetric. We show that the M5-brane with an $R_t$ or an ${\mathrm{AdS}}_3$ factor found previously is half-BPS.