Self-conjugate QCD

Abstract

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 ${\mathbb{R}}^3\times {\mathbb{S}}_L^1$, 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 $\beta$-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 give enough evidence for adiabatic continuity between the small- and large-circle limits.

31 pages; typos fixed, we fixed the symmetry breaking pattern in one example, conclusions remain the same; matches the published version

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Cited by in corpus (11)

• On the baryon-color-flavor (BCF) anomaly in vector-like theories
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Generalized 't Hooft anomalies on non-spin manifolds
• Gauging 1-form center symmetries in simple $SU(N)$ gauge theories
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Deconfinement on axion domain walls
• The gaugino condensate from asymmetric four-torus with twists
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• Condensates and anomaly cascade in vector-like theories
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• Topological terms and anomaly matching in effective field theories on ${\mathbb{R}}^3\times S^1$: I. Abelian symmetries and intermediate scales