$G_2$ holonomy metrics and wrapped D6-branes

We find a one-parameter family of new G_2 holonomy metrics and demonstrate that it can be extended to a two-parameter family. These metrics play an important role as the supergravity dual of the large $N$ limit of four dimensional supersymmetric Yang-Mills. We show that these G_2 holonomy metrics describe the M-theory lift of the supergravity solution describing a collection of D6-branes wrapping the supersymmetric three-cycle of the deformed conifold geometry for any value o...

We construct the supergravity solution in 11 dimensions describing D6-branes wrapped around a Kahler four-cycle with a B-field along the flat directions of the brane. The configuration is dual to an N=2 noncommutative gauge theory in 2+1 dimensions. We also construct the four associated independent Killing spinors. The phenomenon of supersymmetry without supersymmetry appears naturally when compactifying to type IIA or 8d gauged supergravity. Therefore, this solution also pro...

We construct supergravity solutions corresponding to fivebranes wrapping associative three-cycles of constant curvature in manifolds of G_2-holonomy. The solutions preserve 2 supercharges and are first constructed in D=7 gauged supergravity and then lifted to D=10,11. We show that the low-energy theory of M-fivebranes wrapped on a compact hyperbolic three-space is dual to a superconformal field theory in D=3 by exhibiting a flow to an AdS_4 region. For IIB-fivebranes wrapped ...

We obtain a generalisation of the original complete Ricci-flat metric of G_2 holonomy on R^4\times S^3 to a family with a non-trivial parameter \lambda. For generic \lambda the solution is singular, but it is regular when \lambda={-1,0,+1}. The case \lambda=0 corresponds to the original G_2 metric, and \lambda ={-1,1} are related to this by an S_3 automorphism of the SU(2)^3 isometry group that acts on the S^3\times S^3 principal orbits. We then construct explicit supersymmet...

We study a class of D=11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical significance of the supersymmetry constraints and gauge field equations of motion for these spacetimes. We show that the dimensional reduction to D=5 yields known BPS black hole and black string solutions of D=5, N=2 supergravity. The usual ansatz for the dimensional reduction is valid only in the linearized regime of slowly v...

We characterize the geometry produced by M5-branes wrapping a Special Lagrangian 3-cycle in a Calabi-Yau 3-fold. The presence of the brane replaces the the Calabi-Yau by a real manifold with an almost complex structure. We show that, in this classification, a distinguished (1,1) form as well as a globally defined (3,0) form play an important role. The requirements of supersymmetry preservation impose constraints on these structures which can be used to classify the background...

In this talk I discuss intersecting brane configurations coming from explicit metrics with G_2 holonomy. An example of a 7-manifold which representing a R^3 bundle over a self-dual Einstein space is described and the potential appearing after compactification over the 6-d twistor space is derived.

We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special Lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual of pure N=2 super-Yang-Mills theory in D=3. The non-trivial part of the solutions are seven manifolds that admit two G_2 structures each of which is covariantly constant with respect to a different connection with torsion. We derive a form...

We find new supergravity solutions generated by D5-branes wrapping a four-cycle and preserving four and two supersymmetries. We first consider the configuration in which the fivebranes wrap a four-cycle in a Calabi-Yau threefold, which preserves four supersymmetries and is a gravity dual to the Coulomb branch of two-dimensional gauge theories with N=(2,2) supersymmetry. We also study the case of fivebranes wrapping a co-associative four-cycle in a manifold of G_2-holonomy, wh...

We consider supergravity solutions corresponding to D7 branes wrapped on Kahler manifolds with a U(1)_R twist such that some supersymmetry is preserved. We find a class of 1/4-BPS backgrounds where a D7-brane is wrapped on a T^2 torus with a metric of non-constant curvature. Similarly to the flat D7-brane case, the solution has a singularity at finite radius. We also discuss the case where the D7-brane is wrapped on a 4-dimensional non-compact manifold. The field theories o...