Chern-Simons theory on Seifert 3-manifolds

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds Σ by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of non-Abelian flat connections, reduces the complete partition function of the non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold Σ, which is easily evaluated.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.