Thermal and quantum fluctuations in supersymmetric Chern-Simons theory

Abstract

We study radiative corrections to the Abelian self-dual Chern-Simons theory at zero and finite temperatures. 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 is 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 temperatures, 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.