Definable sets, motives and p-adic integrals

We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.Comment: 45 page

Black Ring Deconstruction

We present a sample microstate for a black ring in four and five dimensional language. The microstate consists of a black string microstate with an additional D6-brane. We show that with an appropriate choice of parameters the piece involving the black string microstate falls down a long AdS throat, whose M-theory lift is AdS_3 X S^2. We wrap a spinning dipole M2-brane on the S^2 in the probe approximation. In IIA, this corresponds to a dielectric D2-brane carrying only D0-charge. We conjecture this is the first approximation to a cloud of D0-branes blowing up due to their non-abelian degrees of freedom and the Myers effect.Comment: 10 pages, 2 figure

A Toy Model for Gauge-Mediation in Intersecting Brane Models

We discuss the phenomenology of a toy intersecting brane model where supersymmetry is dynamically broken in an open string hidden sector and gauge-mediated to the visible sector. Scalar masses ~ TeV are easily realizable, and R-symmetry is broken. These ideas are easily generalizable to other intersecting brane models.Comment: 14 pages, LaTeX, references added, some discussion clarifie

Motivic integration and the Grothendieck group of pseudo-finite fields

We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general type depend on p.Comment: 11 page