Geometric superfield approach to superconformal mechanics

Abstract

The new general geometric approach to d=1 conformally invariant systems, previously elaborated by the authors with an example of conformal mechanics, is applied in the supersymmetry case. The authors construct a manifestly invariant superfield description of the superconformal mechanics (SCM) models for arbitrary even N, N being a number of independent real d=1 Poincare supersymmetries. These systems are shown to result from nonlinear realisations of d=1 superconformal groups SU(1,1 mod N/2) in the cosets SU(1,1 mod N/2)/U(N/2). For the N=4 case, which has previously been worked out only on shell, they find two different off-shell formulations related via a duality transformation. The systems with higher N are essentially new. An effect of creating the U(1) central charge in the d=1, N=4 superconformal algebra su(1,1 mod 2) by the duality transformation is revealed. By extending the procedure employed in the bosonic case they derive general superfield solutions of the N=2 and N=4 SCM equations.