Aspects of AdS2 classification in M -theory: solutions with mesonic and baryonic charges

We construct necessary and sufficient geometric conditions for a class of AdS2 solutions of M -theory with, at least, minimal supersymmetry to exist. We generalize previous results in the literature for A1 = (2, 0) supersymmetry in AdS2 to A1 = (1, 0). When the solution can be locally described as AdS2 x 1 g x SE7 with 1 g a Riemann surface of genus g and SE7 a seven-dimensional Sasaki-Einstein manifold, we clarify and unify various solutions present in the literature. In the case of SE7 = Q1,1,1 we find a new solution with baryonic and mesonic charges turned on simultaneously.