Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$

We study Euclidean M2-brane instantons in Freund-Rubin backgrounds $\mathrm{AdS}_{4}\times \mathrm{Y}_7$. For a seven-dimensional weak $G_{2}$ manifold $\mathrm{Y}_7$, we show that the BPS condition for an M2-brane wrapping a three-cycle $Σ\subset \mathrm{Y}_7$ is equivalent to the associativity con