Week 25.01.2009 – 31.01.2009

Phase transitions can often be linked to the spectral properties of certain physical operators. In the theory of the strong interactions the fundamental breaking of chiral symmetry is intimately linked to the spectrum of the Dirac operator. When, however, quarks are favored over anti quarks by means of a chemical potential the Dirac operator becomes non hermitian. In this case the link between the Dirac spectrum and breaking of chiral symmetry has remained a puzzle (The Silver Blaze Problem) for more than two decades. In this talk we discuss how Random Matrix Theory solves this problem.

We construct new exact solutions of pure gravity in five dimensions representing black rings in Taub-NUT spaces, both at zero and at non-zero temperature. We use these solutions to study properties of the D0-D6 system in the supergravity approximation. In particular we compute the interaction energy between D0 and D6 branes, analyze equilibrium configurations and their stability.

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by writing the quaternionic geometry on the hypermultiplet moduli space in terms of twistor geometry. Using this twistor space approach, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.