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Self-conjugate QCD

We carry out a systematic study of $SU(6)$ Yang-Mills theory endowed with fermions in the adjoint and $3$-index antisymmetric mixed-representation. The fermion bilinear in the $3$-index antisymmetric representation vanishes identically, which leads to interesting new phenomena. We first study the theory on a small circle, i.e., on $\mathbb R^3\times \mathbb S^1_L$, employing symmetry-twisted boundary conditions and semi-classical techniques. We find that the ground state is $3$-fold degenerate, which can be explained as a consequence of a $1$-form/$0$-form mixed 't Hooft anomaly. In addition, the theory may admit massless bosonic and fermionic degrees of freedom, depending on the number of flavors, and confines the electric probes in the infrared. Empowered by 't Hooft anomaly matching conditions along with the $2$-loop $β$-function, we further examine the possible infrared symmetry realizations on $\mathbb R^4$ for various number of adjoint and $3$-index antisymmetric fermions. The infrared theory is either a conformal field theory, which is expected for a large number of flavors, or it is confining with or without chiral symmetry breaking. In a few cases, we are able to g