Critical scaling dimension for D-module reps of N=4,5,7 superconformal algebras and constraints on superconformal mechanics
The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the one-dimensional N-Extended Supersymmetry Algebra induce D-module representations, with a given scaling dimension lambda, for the N=2,4,8 superconformal algebras. For N=4 the exceptional D(2,1|alpha) superalgebras are recovered for alpha = (2-k) lambda. For N=8, the four superconformal algebras are recovered for different k's (with kneq 4) at critical values of the scaling dimension lambda. Superconformal mechanics (both single and multiparticle) in a Lagrangian framework is derived from D-module reps with a standard method. The existence of critical values of the scaling dimension implies non-trivial constraints on the admissible superconformal models. This talk is based on JMP 53, 043513 (2012) and a work in progress.