Programme

Quantum critical points in condensed matter systems can exhibit anisotropic scaling. Lifshitz geometries have been proposed that could holographically described such systems. I will describe top down constructions of Lifshitz geometries in both type IIB and D=11 supergravity: there are infinite classes of solutions associated with Sasaki-Einstein geometry and another solution associated with a new consistent KK truncation of D=11 supergravity on the product of a four-sphere with a three-dimensional Einstein space.

We calculate the first-order backreaction of a stack of anti-D3 branes placed at the bottom of the Klebanov-Strassler solution, and find that if a certain singularity in the infrared of this solution is not acceptable these anti-D3 branes source non-normalizable modes. This in turn affects the lifting of certain AdS vacua to dS vacua using anti-D3 branes, and can invalidate many string cosmology constructions.

Disk amplitudes for massless closed string emission from D-brane bound states can reproduce the non-trivial features of known two-charge supergravity solutions, which are conjectured to have an interpretation as classical microstates of a black hole. I will present these results in the D1-D5 and D5-P duality frames and describe work in progress on generalizing these results to the three-charge black hole system.

The spectrum of BPS states in N=2 string vacua is known to jump across certain walls of marginal stability in moduli space. The discontinuity of the BPS degeneracies is governed by wall-crossing formulae established independently by Kontsevich-Soibelman and Joyce-Song. I shall review these formulae in physical language, and interpret their predictions in terms of the supersymmetric quantum mechanics of multi-centered BPS configurations. Work in progress with A. Sen and J. Manschot.

The work of Vafa and Strominger back to 1996 was a major breakthrough in black hole entropy counting. They were able to count the microscopic states of the black hole and found precise agreement with the Beckenstein-Hawking entropy. This matching only worked when all charges were very large and the dichotomy black hole degeneracy versus BPS states index was never very well understood. Here we address some of these problems. First we define some black hole index and then using AdS3/CFT2 correspondence we are able to compute the black hole degeneracies based on anomalies and Chern-Simons terms. The results are exact and incorporate all finite charge quantum corrections in the limit when one of the charges is taken to be very large while keeping the others finite. Precise agreement between microscopics and macroscopics counting is found for several examples of four and five dimensional black holes.

We reformulate M-theory to make duality a manifest symmetry of the action using the generalized geometry that we derive from considering membrane T-duality