2002/05/31 by Jerome P. Gauntlett, Dario Martelli, Stathis Pakis +1 · 2 citations
Physics and Astronomy · Mathematics · #hep-th #math.DG
paper · pdf · doi:10.1007/s00220-004-1066-y
published as Commun.Math.Phys. 247 (2004) 421-445 · 29 pages. v2: typos fixed, references added, and Discussion expanded
arxiv created 2002/06/10 · arxiv updated 2009/11/30
We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form R1,9-n x Mn with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS fivebrane geometries. We concentrate on the case d=7, preserving two or four supersymmetries, corresponding to branes wrapped on associative or SLAG three-cycles. Given the existence of Killing spinors, we show that M7 admits a G2-structure or an SU(3)-structure, respectively, of specific type. We also prove the converse result. We use the existence of these geometric structures as a new technique to derive some known and new explicit solutions, as well as a simple theorem implying that we have vanishing NS three-form and constant dilaton whenever M7 is compact with no boundary. The analysis extends simply to other type II examples and also to type I supergravity.