We study a variational problem whose critical point determines the Reeb vector field for a SasakiEinstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the EinsteinHilbert action, restricted to a space of Sasakian metrics on a link <i>L</i> in a CalabiYau cone <i>X</i>, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the DuistermaatHeckman formula and also to a limit of a certain equivariant index on <i>X</i> that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of a SasakiEinstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension <i>n</i>=3 these results provide, via AdS

We show that the spinning magnetic one-brane in minimal five-dimensional supergravity admits a decoupling limit that interpolates smoothly between a self-dual null orbifold of AdS_3 \times S^2 and the near-horizon limit of the extremal Kerr black hole times a circle. We use this interpolating solution to understand the field theory dual to spinning M5 branes as a deformation of the Discrete Light Cone Quantized (DLCQ) Maldacena-Stominger-Witten (MSW) CFT. In particular, the conformal weights of the operators dual to the deformation around AdS_3 \times S^2 are calculated. We present pieces of evidence showing that a CFT dual to the four-dimensional extremal Kerr can be obtained from the deformed MSW CFT.

We show that the six-dimensional uplift of the five-dimensional Near-Horizon-Extremal-Kerr (NHEK) spacetime can be obtained from an AdS_3 X S^3 solution by a sequence of supergravity - but not string theory - dualities. We present three ways of viewing these pseudo-dualities: as a series of transformations in the STU model, as a combination of Melvin twists and T-dualities and, finally, as a sequence of two generalized spectral flows and a coordinate transformation. We then use these to find an infinite family of asymptotically flat embeddings of NHEK spacetimes in string theory, parameterized by the arbitrary values of the moduli at infinity. Our construction reveals the existence of non-perturbative deformations of asymptotically-NHEK spacetimes, which correspond to the bubbling of nontrivial cycles wrapped by flux, and paves the way for finding a microscopic field theory dual to NHEK which involves Melvin twists of the D1-D5 gauge theory. Our analysis also clarifies the meaning of the generalized spectral flow solution-generating techniques that have been recently employed in the literature.

We define new energy momentum surface density and quasilocal mass for the boundary surface of a spacelike region in spacetime. Isometric embeddings of such a surface into the Minkowski space are used as reference surfaces in the definition. When the reference surface lies in a flat three-dimensional space slice of the Minkowski space, our expression recovers the Brown-York and Liu-Yau quasilocal mass. Moreover, we prove the positivity of the new quasilocal mass under the dominant energy condition and show that it is zero for surfaces in the Minkowski space.

We describe the counting of BPS states of Type II on K3 by relating the supersymmetric cycles of genus <i>g</i> to the number of rational curves with <i>g</i> double points on K3. The generating function for the number of such curves is the left-moving partition function of the bosonic string.