Two Outcomes for Two Old (Super-)Problems

I briefly review the outcomes of two very different old questions -- where global SUSY improves on ordinary QFT -- when they are in turn posed in the local, SUGRA, context. The first concerns the unexpectedly powerful role of the "Dirac square root" graded algebra relation $E=Q^2$, originally found in D=4 SUSY by Gol'fand and Likhtman, in proving positive energy theorems both in SUGRA and in ordinary gravity theories, where $E$ and $Q$ have very different -- gauge generator -- definitions. The second seeks SUGRA counterparts of the boson/fermion loop ultraviolet cancellations in SUSY models. Here the result is negative: local supersymmetry cannot overcome the infinities associated with the dimensional gravitational $\kappa^2$ even, as recently shown, in maximal D=11 SUGRA.