Supersymmetric AdS _{3} × S ^{2} Mtheory geometries with fluxes
Abstract
Motivated by a recent observation that the LLM geometries admit 1/4BPS M5brane probes with worldvolume AdS _{3} × Σ_{2} × S ^{1} preserving the Rsymmetry, SU(2) × U(1), we initiate a classification of the most general AdS _{3}× S ^{2} geometries in Mtheory dual to twodimensional chiral mathcal{N} = left( {4,0} right) SCFTs. We retain all field strengths consistent with symmetry and derive the torsion conditions for the internal sixmanifold, 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. With the torsion conditions derived, we establish the MSW solution as the only solution in the class where M6 is an SU(3)structure manifold. Then, specialising to the case where the spinors define an SU(2)structure, we note that supersymmetry dictates that all magnetic fluxes necessarily thread the S ^{2}. 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2010
 DOI:
 10.1007/JHEP08(2010)114
 arXiv:
 arXiv:1005.4527
 Bibcode:
 2010JHEP...08..114O
 Keywords:

 Supergravity Models;
 MTheory;
 High Energy Physics  Theory
 EPrint:
 32 pages, minor corrections