Supercurrents and (Partial) Supersymmetry in Adjoint QCD${}_2$ and Its Generalizations

Abstract

$1+1$-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 $\sqrt{\frac{g^{2}N}{2\ddot{I}€}}$ it exhibits supersymmetry. In this paper, we obtain a deeper insight into how the supersymmetry works by constructing the gauge invariant, Lorentz covariant supercurrent $j_{\hat{I}¼A}$. 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 $\sqrt{\frac{3g^{2}N}{2\ddot{I}€}}$.

41 pages; v2 minor improvements, refs added; v3 minor improvements