CRITICAL D-MODULE REPS FOR FINITE SUPERCONFORMAL ALGEBRAS AND THEIR SUPERCONFORMAL MECHANICS
The simple finite Lie superalgebras D(2, 1; α), G(3), D(4, 1), D(2, 2), A(3, 1) and F(4) admit D-module representations, given by a set of differential operators of a single variable t ∈ ℝ, at a critical value of the scaling dimension λ. These superalgebras are one-dimensional N-extended superconformal algebras with N = 4 (D(2, 1; α)), N = 7 (G(3)) and N = 8 (the remaining ones). The critical D-module reps induce invariant actions in the Lagrangian framework for superconformal mechanics in D target dimensions. The N = 8 critical scalings 
