Supersymmetric AdS3 X S2 M-theory geometries with fluxes

TL;DR

This work develops a general Killing spinor analysis to classify supersymmetric $AdS_3 \times S^2$ geometries in M-theory, deriving comprehensive torsion conditions for the internal $M_6$ from two independent spinors and exploring both $SU(3)$- and $SU(2)$-structure branches. It shows that the MSW solution emerges in the $SU(3)$ case, while for $SU(2)$-structure, supersymmetry constrains fluxes such that the magnetic flux on $S^2$ dominates and the four-form flux along $M_6$ vanishes, reducing to a known wrapped-brane class with an LLM-like spinor relation. The analysis reveals two Killing directions generating full symmetry of the warp factors and fluxes, with a third internal Killing direction not yielding a complete symmetry unless additional spinor-norm conditions are met. The results establish a rigorous framework for further finding explicit regular solutions and for connecting back-reacted M5-brane probes to broader holographic contexts, including potential interpolations with LLM geometries.

Abstract

Motivated by a recent observation that the LLM geometries admit 1/4-BPS M5-brane probes with worldvolume AdS3 X Σ_2 X S1 preserving the R-symmetry, we initiate a classification of the most general AdS3 X S2 geometries in M-theory. We retain all field strengths consistent with symmetry and derive the torsion conditions for M_6 in terms of two linearly independent spinors. Surprisingly, we identify three Killing directions for M_6, but only two of these generate isometries of the overall ansatz. We show that the existence 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 the class of solutions is 1/4-BPS, we note that supersymmetry dictates that all magnetic fluxes necessarily thread the S2. Finally, by assuming that the two remaining Killing directions are parallel and aligned with one of the two vectors defining the SU(2)-structure, we derive a general relationship for the two spinors before extracting a known class of solutions from the torsion conditions.