Exact gravitational plane waves and two-dimensional gravity

We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves and, for generic initial data, produce a spacetime singularity at the focusing hypersurface. There is, in addition, an infinite family of regular solutions and an intriguing static geometry supported by scalar fields. Upon dimensional reduction, the theory can be viewed as an exactly solvable two-dimensional gravity model. This provides a new viewpoint on the gravitational dynamics. Finally, we comment on a simple mechanism by which short-distance corrections in the two-dimensional model can remove the singularity.Comment: 8 page

N=2 gauge theories and quantum phases

The partition function of general N = 2 supersymmetric SU(2) Yang-Mills theories on a four-sphere localizes to a matrix integral. We show that in the decompactification limit, and in a certain regime, the integral is dominated by a saddle point. When this takes effect, the free energy is exactly given in terms of the prepotential, $F=-R^2 Re (4\pi i {\cal F})$, evaluated at the singularity of the Seiberg-Witten curve where the dual magnetic variable $a_D$ vanishes. We also show that the superconformal fixed point of massive supersymmetric QCD with gauge group SU(2) is associated with the existence of a quantum phase transition. Finally, we discuss the case of N=2* SU(2) Yang-Mills theory and show that the theory does not exhibit phase transitions.Comment: 23 pages, 4 figure

D=2+1 N=2 Yang-Mills Theory From Wrapped Branes

We find a new solution of Type IIB supergravity which represents a collection of D5 branes wrapped on the topologically non-trivial S^3 of the deformed conifold geometry T^*S^3. The Type IIB solution is obtained by lifting a new solution of D=7 SU(2)_L x SU(2)_R gauged supergravity to ten dimensions in which SU(2)_D gauge fields in the diagonal subgroup are turned on. The supergravity solution describes a slice of the Coulomb branch in the large N limit of N=2 SYM in three dimensions.Comment: 19 pages, 1figure, harvmac; expanded analysis of D=4 N=2 system in the appendix, references adde