Instantons in Supersymmetric Quantum Mechanics

Abstract

The rôle of classical solutions in supersymmetric field theories is a very intriguing one. A few phenomena in supersymmetric theories which bear witness to this are the following. The generation of central charges in the supersymmetry algebra from topological charges connected with solitons and monopoles, as in the two-dimensional Wess-Zumino model and the four-dimensional N = 4 supersymmetric Yang-Mills theory1). The breaking of supersymmetry. Instanton effects can lead to supersymmetry breaking, because instantons may connect fermionic states in one topological sector of the theory to bosonic states in another one2),3). The quantum corrections to the mass of the particles corresponding to classical extended objects seem to vanish in various cases, indicating the almost unchanged persistence of these objects in the quantum theory. This takes place, e.g., for the solitons in the three-dimensional CPN-1 model4) Finally, a more speculative possibility is that the well-known vanishing of the (3 function of N = 4 Yang-Mills theory results from the theory describing a gas of non-interacting monopoles. Indications of a similar behaviour in the much simpler model of supersymmetric quantum mechanics are discussed below. KeywordsSupersymmetry BreakingTopological ChargeSupersymmetric TheorySupersymmetry AlgebraFermion NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.