What the study found
The study finds that adjoint QCD2, a 1+1-dimensional SU(N) gauge theory with an adjoint Majorana fermion, has supersymmetry at a specific fermion mass. The authors also identify related generalizations where a supersymmetric massive sector can appear, and in some cases both the massive and gapless sectors are supersymmetric.
Why the authors say this matters
The authors conclude that constructing a gauge-invariant, Lorentz-covariant supercurrent gives a deeper understanding of how the supersymmetry works. They also suggest that the generalized models show how supersymmetry can appear in both massive and non-supersymmetric conformal field theory sectors, and in some cases in both sectors together.
What the researchers tested
The researchers constructed the gauge-invariant, Lorentz-covariant supercurrent j_μ^A for adjoint QCD2 and examined how its conservation depends on a quantum anomaly. They then extended the construction to a class of gauge theories with an adjoint Majorana fermion of an appropriate mass plus additional massless fermions, allowing the gauge group to be more general than SU(N).
What worked and what didn't
For adjoint QCD2, supersymmetry appears at fermion mass sqrt(g^2N/2π). In the generalized models, the authors report that there is generally a supersymmetric massive sector and a non-supersymmetric conformal field theory sector, but they also identify cases where both sectors are supersymmetric; one example is SU(N) gauge theory with three adjoint Majorana fermions, two massless and one with mass sqrt(3g^2N/2π).
What to keep in mind
The abstract does not describe experimental data, numerical tests, or the full derivation, so only the stated theoretical results can be summarized here. It also does not give limitations beyond the fact that the supersymmetry appears at specific mass values and in specific classes of models.
Key points
- Adjoint QCD2 has supersymmetry at fermion mass sqrt(g^2N/2π).
- The authors construct a gauge-invariant, Lorentz-covariant supercurrent.
- The supercurrent conservation relies on a quantum anomaly.
- Generalized models can have a supersymmetric massive sector and a non-supersymmetric conformal field theory sector.
- A fully supersymmetric gapless example is SU(N) gauge theory with three adjoint Majorana fermions.
Disclosure
- Research title:
- Adjoint QCD2 can exhibit supersymmetry at special fermion masses
- Authors:
- Igor R. Klebanov, Silviu S. Pufu, Benjamin T. Søgaard, Edward Witten
- Institutions:
- Princeton University, Princeton University, Princeton University
- Publication date:
- 2026-04-27
- OpenAlex record:
- View
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