M2-doughnuts

We present a family of new M2-brane solutions in $AdS_7\times S^4$ that calculate toroidal BPS surface operators in the $\mathcal{N}=(2,0)$ theory. These observables are conformally invariant and not subject to anomalies so we are able to evaluate their finite expectation values at leading order at large $N$. In the limit of a thin torus we find a cylinder, which is a natural surface generalization of both the circular and parallel lines Wilson loop. We study and comment on this limit in some detail.