PARTIAL SUPERSYMMETRY BREAKING IN N = 4 SUPERSYMMETRIC QUANTUM-MECHANICS

We present a simple d = 1 model of N = 4 supersymmetric quantum mechanics (SQM) in which N = 4 supersymmetry can be spontaneously broken down to N = 2. When both SU(2) automorphism symmetries of N = 4 1D supertranslation algebra are explicitly broken, this superalgebra acquires a constant central charge proportional to the product of two SU(2) breaking parameters. Due to this crucial property, no contradiction arises with Witten's theorem forbidding the partial spontaneous supersymmetry breaking in SQM models based on standard (having no central charges) 1D supertranslation algebras. For the partial breaking to really come about, it also proves necessary to consider the most general class of N = 4, d = 1 SQM Hamiltonians involving the terms quartic in fermion fields. We show that after performing a duality transformation these models can be interpreted as resulting from certain U(1) invariant N = 2 2D Kahler sigma models via the Scherk-Schwartz-type dimensional reduction.