Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure

Milankovitch-paced erosion in the southern Central Andes

It has long been hypothesized that climate can modify both the pattern and magnitude of erosion in mountainous landscapes, thereby controlling morphology, rates of deformation, and potentially modulating global carbon and nutrient cycles through weathering feedbacks. Although conceptually appealing, geologic evidence for a direct climatic control on erosion has remained ambiguous owing to a lack of high-resolution, long-term terrestrial records and suitable field sites. Here we provide direct terrestrial field evidence for long-term synchrony between erosion rates and Milankovitch-driven, 400-kyr eccentricity cycles using a Plio-Pleistocene cosmogenic radionuclide paleo-erosion rate record from the southern Central Andes. The observed climate-erosion coupling across multiple orbital cycles, when combined with results from the intermediate complexity climate model CLIMBER-2, are consistent with the hypothesis that relatively modest fluctuations in precipitation can cause synchronous and nonlinear responses in erosion rates as landscapes adjust to ever-evolving hydrologic boundary conditions imposed by oscillating climate regimes

Computational and Mathematical Organization Theory Affiliation of Authors

January 2004: Special Issue on Mathematical representations for the analysis of social networks within and between organization