Supersymmetric AdS3 X S2 M-theory geometries with fluxes

TL;DR

This paper classifies the most general AdS3 X S2 geometries in M-theory with fluxes, revealing new insights into supersymmetric solutions and their geometric structures, especially in the context of 1/4-BPS configurations.

Contribution

It provides a comprehensive classification of AdS3 X S2 geometries in M-theory, including torsion conditions and the role of spinor structures, extending previous understanding of supersymmetric flux backgrounds.

Findings

Identified three Killing directions in M6, with only two generating isometries.

Supersymmetry requires magnetic fluxes to thread the S2 in 1/4-BPS solutions.

Derived a general relationship for spinors under specific geometric assumptions.

Abstract

Motivated by a recent observation that the LLM geometries admit 1/4-BPS M5-brane probes with worldvolume AdS3 X \Sigma_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.