Investigations in Planar Physics

The research described in this thesis is divided into two parts. The first part concerns the calculation of quantum and thermal corrections to a supersymmetric Chern-Simons field theory. The second part studies Chern -Simons solitons in 2+1 dimensional Einstein gravity. In Chapter I we study radiative corrections to the Abelian self-dual Chern-Simons theory at zero and finite temperature. The analysis is performed with the help of functional methods. We consider the supersymmetric extension of scalar matter fields minimally coupled to a gauge field whose dynamics are governed solely by the Chern-Simons term. The scalar field potential is a self-dual sixth order polynomial with U(1)-symmetry-breaking and symmetry -preserving minima which are degenerate. We find that the zero-temperature one-loop radiative corrections do not remove this degeneracy and both minima remain supersymmetric. We calculate the leading-order finite-temperature contributions to the effective potential in the high-temperature limit and we find that the U(1)-symmetry is restored. In contrast to four-dimensional field theories that restore the U(1) -symmetry at high-temperature, the restoration of the U(1) -symmetry in the abelian self-dual Chern-Simons theory occurs at the two-loop level. The Chern-Simons system without supersymmetry is discussed, as well as the scalar field model without Chern-Simons gauge fields. The same finite temperature result emerges in these cases. In Chapter II we consider the Abelian Chern-Simons -Higgs model in 2+1 dimensional curved space. We obtain coupled nonlinear differential equations for the Einstein -scalar-gauge field equations. The equations are solved numerically to obtain topological soliton solutions. These solitons have mass and angular momentum. Numerical results show that space-time created by these solitons do not possess closed time-like curves, unlike that of spinning point particles. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 01239-4307. Ph. 617-253-5668; Fax 617-253-1690.).