Gauge theory of Riemann ellipsoids

Abelian Gauge Theory on Riemann Surfaces

An Abelian gauge eld theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the rst Chern class c 1 (L) and by a certain intersection number obtained fro...

Stability Properties of the Riemann Ellipsoids

We study the ellipticity and the “Nekhoroshev stability” (stability properties for finite, but very long, time scales) of the Riemann ellipsoids. We provide numerical evidence that the regions of ellipticity of the ellipsoids of types II and III are larger than those found by Chandrasekhar in the 60’s and that all Riemann ellipsoids, except a finite number of codimension one subfamilies, are Ne...

Abelian Gauge Theory on Riemann Surfaces and New Topological Invariants

Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations

We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two equal axes.

One-Loop Riemann Surfaces in Schnabl Gauge

Due to a peculiar behavior at the open string midpoint, loop diagrams in Schnabl gauge were expected to fail to produce the relevant closed string moduli. We find that closed string moduli are generated because the Riemann surfaces are built with slanted wedges: semi-infinite strips whose edges have parameterizations related by scaling. We examine in detail one-loop string diagrams and find tha...