Supercurrents and (Partial) Supersymmetry in Adjoint QCD$_2$ and Its Generalizations
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2025
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| _version_ | 1866913158495469568 |
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| author | Klebanov, Igor R. Pufu, Silviu S. Søgaard, Benjamin Witten, Edward |
| author_facet | Klebanov, Igor R. Pufu, Silviu S. Søgaard, Benjamin Witten, Edward |
| contents | $1+1$-dimensional $SU(N)$ gauge theory coupled to an adjoint Majorana fermion, also known as adjoint QCD$_2$, has the surprising feature that at fermion mass $\sqrt{\frac{g^2 N}{2 π}}$ it exhibits supersymmetry. In this paper, we obtain a deeper insight into how the supersymmetry works by constructing the gauge invariant, Lorentz covariant supercurrent $j_{μA}$. Its conservation relies crucially on the presence of a quantum anomaly. We generalize this construction to a class of models where, in addition to an adjoint Majorana fermion of an appropriate mass, the gauge theory is coupled to some collection of massless fermions ($SU(N)$ may be replaced by a more general gauge group). In general, these models have a supersymmetric massive sector and a non-supersymmetric CFT sector [arXiv:2202.04017], but there are cases in which both sectors are supersymmetric. An example of such a gapless, fully supersymmetric model is $SU(N)$ gauge theory coupled to three adjoint Majorana fermions, of which two are massless and the third has mass $\sqrt{\frac{3g^2 N}{2π}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supercurrents and (Partial) Supersymmetry in Adjoint QCD$_2$ and Its Generalizations Klebanov, Igor R. Pufu, Silviu S. Søgaard, Benjamin Witten, Edward High Energy Physics - Theory $1+1$-dimensional $SU(N)$ gauge theory coupled to an adjoint Majorana fermion, also known as adjoint QCD$_2$, has the surprising feature that at fermion mass $\sqrt{\frac{g^2 N}{2 π}}$ it exhibits supersymmetry. In this paper, we obtain a deeper insight into how the supersymmetry works by constructing the gauge invariant, Lorentz covariant supercurrent $j_{μA}$. Its conservation relies crucially on the presence of a quantum anomaly. We generalize this construction to a class of models where, in addition to an adjoint Majorana fermion of an appropriate mass, the gauge theory is coupled to some collection of massless fermions ($SU(N)$ may be replaced by a more general gauge group). In general, these models have a supersymmetric massive sector and a non-supersymmetric CFT sector [arXiv:2202.04017], but there are cases in which both sectors are supersymmetric. An example of such a gapless, fully supersymmetric model is $SU(N)$ gauge theory coupled to three adjoint Majorana fermions, of which two are massless and the third has mass $\sqrt{\frac{3g^2 N}{2π}}$. |
| title | Supercurrents and (Partial) Supersymmetry in Adjoint QCD$_2$ and Its Generalizations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.17138 |