FLUCTUATION EQUATIONS ABOUT CLASSICAL FIELD CONFIGURATIONS AND SUPERSYMMETRIC QUANTUM-MECHANICS

Several (1 + 1)-dimensional nonlinear field theory models are considered and the solutions of the small fluctuation equations about their static, classical, finite energy configurations are derived. The models investigated are scalar field theories with sine-Gordon, double-well, and inverted double-well potentials, and the 0(3) nonlinear sigma model with symmetry-breaking sine-Gordon term. All models are considered on a circle, so that the fluctuation equations are of Lameé type. In each case the supersymmetric partner is then constructed and the spectra and solutions are investigated. It is found that the two fluctuation equations about the sphaleron configuration of the 0(3) nonlinear sigma model are not supersymmetric partners except when the circle becomes of infinite extent. Further aspects investigated are the behaviour of the Witten index and the breaking of supersymmetry under antiperiodic boundary conditions. © 1993 Academic Press, Inc.