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Motivated by a recent observation that the LLM geometries admit 1/4-BPSM5-brane probes with worldvolume AdS3 X \Sigma_2 X S1 preserving theR-symmetry, we initiate a classification of the most general AdS3 X S2geometries in M-theory. We retain all field strengths consistent with symmetryand derive the torsion conditions for M_6 in terms of two linearly independentspinors. Surprisingly, we identify three Killing directions for M_6, but onlytwo of these generate isometries of the overall ansatz. We show that theexistence of this third direction depends on the norm of the spinors. Then,specialising to the case where the spinors define an SU(2)-structure and theclass of solutions is 1/4-BPS, we note that supersymmetry dictates that allmagnetic fluxes necessarily thread the S2. Finally, by assuming that the tworemaining Killing directions are parallel and aligned with one of the twovectors defining the SU(2)-structure, we derive a general relationship for thetwo spinors before extracting a known class of solutions from the torsionconditions.

Supersymmetric AdS3 X S2 M-theory geometries with fluxes