Investigations in Planar Physics
Abstract
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 ChernSimons 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 selfdual ChernSimons 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 ChernSimons term. The scalar field potential is a selfdual sixth order polynomial with U(1)symmetrybreaking and symmetry preserving minima which are degenerate. We find that the zerotemperature oneloop radiative corrections do not remove this degeneracy and both minima remain supersymmetric. We calculate the leadingorder finitetemperature contributions to the effective potential in the hightemperature limit and we find that the U(1)symmetry is restored. In contrast to fourdimensional field theories that restore the U(1) symmetry at hightemperature, the restoration of the U(1) symmetry in the abelian selfdual ChernSimons theory occurs at the twoloop level. The ChernSimons system without supersymmetry is discussed, as well as the scalar field model without ChernSimons gauge fields. The same finite temperature result emerges in these cases. In Chapter II we consider the Abelian ChernSimons Higgs model in 2+1 dimensional curved space. We obtain coupled nonlinear differential equations for the Einstein scalargauge field equations. The equations are solved numerically to obtain topological soliton solutions. These solitons have mass and angular momentum. Numerical results show that spacetime created by these solitons do not possess closed timelike curves, unlike that of spinning point particles. (Copies available exclusively from MIT Libraries, Rm. 140551, Cambridge, MA 012394307. Ph. 6172535668; Fax 6172531690.).
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT........12I
 Keywords:

 EINSTEIN GRAVITY;
 Physics: Elementary Particles and High Energy