Loops in supergroups

We study the theory of a scalar in the fundamental representation of the internal supergroup $SU(N|M)$. Remarkably, for $M=N+1$ its tree-level mass does not receive quantum corrections at one loop from either self-coupling or interactions with gauge bosons and fermions. This property comes at the price of introducing both degrees of freedom with wrong statistics and with wrong sign kinetic terms. We detail a method to break $SU(N|M)$ down to its bosonic subgroup through a Higgs-like mechanism, allowing for the partial decoupling of the dangerous modes, and study the associated vacuum structure up to one loop.