We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kähler 6-manifolds, nearly parallel G2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.

We present NS1+NS5-brane solutions of heterotic supergravity on curved geometries. They interpolate between a near horizon AdS 3 × X k × T 7−k region andThe solutions require first-order α -corrections to the field equations, and special point-like instantons play an important role, whose singular support is a calibrated submanifold wrapped by the NS5-brane. It is also possible to add a gauge anti-fivebrane. We determine the super isometries of the near horizon geometry, which are supposed to appear as symmetries of the holographically dual two-dimensional conformal field theory.e-print archive: http://lanl.arXiv.org/abs/1202.5046 772 KARL-PHILIP GEMMER ET AL.

We consider compactifications of heterotic supergravity on anti-de Sitter space, with a six-dimensional nearly Kähler manifold as the internal space. Completing the model proposed by Frey and Lippert [10] with the particular choice of SU(3)/U(1)×U(1) for the internal manifold, we show that it satisfies not only the supersymmetry constraints but also the equations of motion with string corrections of order α ′. Furthermore, we present a nonsupersymmetric model. In both solutions we find confirmed a recent result of Ivanov [18] on the connection used for anomaly cancellation. Interestingly, the volume of the internal space is fixed by the supersymmetry constraints and/or the equations of motion.

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly Kähler manifold. The cone over the sinecone on a nearly Kähler manifold has holonomy group Spin(7) and can be foliated by submanifolds with either holonomy group G2, a nearly parallel G2-structure or a cocalibrated G2-structure. We show that there is a G2-instanton on each of these seven-dimensional manifolds which gives rise to a Spin(7)-instanton in eight dimensions. The well-known octonionic instantons on R 7 and R 8 are contained in our construction as the special cases of an instanton on the cone and on the cone over the sine-cone, both over the six-sphere, respectively.

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