Effective Lagrangians for (0+1) and (1+1) dimensionally reduced versions of D=4, N=2 SYM theory Original Research Article

We consider dimensionally reduced versions of N=2 four-dimensional supersymmetric Yang–Mills theory and determine the one-loop effective Lagrangians associated with the motion over the corresponding moduli spaces. In the (0+1) case, the effective Lagrangian describes an N=4 supersymmetric quantum mechanics of the Diaconescu–Entin type. In (1+1) dimensions, the effective Lagrangian represents a twisted N=4 supersymmetric σ model due to Gates, Hull and Roĉek. We discuss the genetic relationship between these two models and present the explicit results for all gauge groups.