Adjoint QCD2 can show supersymmetry and supercurrents

What the study found: The authors report that 1+1-dimensional SU(N) gauge theory with an adjoint Majorana fermion, called adjoint QCD2, has supersymmetry at a specific fermion mass. They also construct a gauge-invariant, Lorentz-covariant supercurrent and generalize the construction to related gauge theories with additional massless fermions.
Why the authors say this matters: The study suggests that understanding the supercurrent gives a deeper picture of how supersymmetry works in these theories. The authors also conclude that some generalized models contain a supersymmetric massive sector, and in some cases both the massive and gapless sectors are supersymmetric.
What the researchers tested: The researchers studied two-dimensional SU(N) gauge theory coupled to an adjoint Majorana fermion, and then extended the analysis to models with an adjoint Majorana fermion plus collections of massless fermions, with SU(N) replaceable by more general gauge groups. They focused on constructing the supercurrent and examining when supersymmetry appears.
What worked and what didn't: In adjoint QCD2, supersymmetry appears when the fermion mass equals sqrt(g^2N/2π). The supercurrent conservation depends crucially on a quantum anomaly. In the generalized class of models, the massive sector is generally supersymmetric, while the conformal field theory (CFT) sector is generally not; however, the abstract gives an example with three adjoint Majorana fermions, two massless and one massive with mass sqrt(3g^2N/2π), in which the model is fully supersymmetric.
What to keep in mind: The abstract does not describe experimental data, numerical methods, or detailed proofs. It also does not specify which generalized models beyond the stated examples have both sectors supersymmetric.

Key points

• Adjoint QCD2 shows supersymmetry at fermion mass sqrt(g^2N/2π).
• The authors construct a gauge-invariant, Lorentz-covariant supercurrent for the theory.
• Supercurrent conservation relies crucially on a quantum anomaly.
• In generalized models, the massive sector is generally supersymmetric, while the CFT sector is generally not.
• A fully supersymmetric example is SU(N) gauge theory with three adjoint Majorana fermions, two massless and one massive.