TY - JOUR
T1 - Supersymmetric AdS3 × S2 M-theory geometries with fluxes
AU - Colgáin, Eoin Ó
AU - Wua, Jun Bao
AU - Yavartanoo, Hossein
PY - 2010
Y1 - 2010
N2 - Motivated by a recent observation that the LLM geometries admit 1/4-BPS M5-brane probes with worldvolume AdS3 × Σ2 × S1 preserving the R-symmetry, SU(2) × U(1), we initiate a classification of the most general AdS3×S2 geometries in M-theory dual to two-dimensional chiral N = (4, 0) SCFTs. We retain all field strengths consistent with symmetry and derive the torsion conditions for the internal six-manifold, M6, in terms of two linearly independent spinors. Surprisingly, we identify three Killing directions for M6, 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 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.
AB - Motivated by a recent observation that the LLM geometries admit 1/4-BPS M5-brane probes with worldvolume AdS3 × Σ2 × S1 preserving the R-symmetry, SU(2) × U(1), we initiate a classification of the most general AdS3×S2 geometries in M-theory dual to two-dimensional chiral N = (4, 0) SCFTs. We retain all field strengths consistent with symmetry and derive the torsion conditions for the internal six-manifold, M6, in terms of two linearly independent spinors. Surprisingly, we identify three Killing directions for M6, 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 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.
KW - M-Theory
KW - Supergravity Models
UR - http://www.scopus.com/inward/record.url?scp=80053167582&partnerID=8YFLogxK
U2 - 10.1007/JHEP08(2010)114
DO - 10.1007/JHEP08(2010)114
M3 - Article
AN - SCOPUS:80053167582
SN - 1126-6708
VL - 2010
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 8
M1 - 114
ER -