SUBATECH–2002–25 Effective Lagrangians for (0 + 1) and (1 + 1)

We consider dimensionally reduced versions ofN = 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 supesymmetric quantum mechanics of the Diaconescu– Entin type. In (1+ 1) dimensions, the effective Lagrangian represents a twisted N = 4 supesymmetric 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.