Loops in supergroups

TL;DR

This paper investigates scalar fields in supergroup gauge theories, revealing a special case where the mass remains uncorrected at one loop, and explores symmetry breaking mechanisms to manage problematic modes.

Contribution

It introduces a method to break supergroup symmetry to its bosonic subgroup and analyzes the vacuum structure at one loop, highlighting unique quantum correction properties.

Findings

Scalar in SU(N|M) with M=N+1 has mass protected at one loop.

A Higgs-like mechanism can break supergroup symmetry to bosonic subgroup.

Partial decoupling of problematic modes is achieved through vacuum analysis.

Abstract

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.