Generalized 't Hooft anomalies on non-spin manifolds

Abstract

We study the mixed anomaly between the discrete chiral symmetry and general baryon-color-flavor (BCF) backgrounds in $SU(N_c)$ gauge theories with $N_f$ flavors of Dirac fermions in representations ${\mathcal{R}}_c$ of $N$-ality $n_c$, formulated on non-spin manifolds. We show how to study these theories on ${\mathbb{CP}}^2$ by turning on general BCF fluxes consistent with the fermion transition functions. We consider several examples in detail and argue that matching the anomaly on non-spin manifolds places stronger constraints on the infrared physics, compared to the ones on spin manifolds (e.g.~${\mathbb{T}}^4$). We also show how to consistently formulate various chiral gauge theories on non-spin manifolds.

arXiv comment27 pages; minor corrections, references added, matches the published version

References in corpus (41)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Generalized Global Symmetries
• Theta, Time Reversal, and Temperature
• Orientifold theory dynamics and symmetry breaking
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Minimal Walking on the Lattice
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Dijet Cross Sections and Parton Densities in Diffractive DIS at HERA
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Evolution of the coupling constant in SU(2) lattice gauge theory with two adjoint fermions
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• The infrared dynamics of Minimal Walking Technicolor
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Anomaly constraints on deconfinement and chiral phase transition
• A New SU(2) Anomaly
• Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Two-flavor adjoint QCD
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• C-P-T anomaly matching in bosonic quantum field theory and spin chains
• Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
• On the baryon-color-flavor (BCF) anomaly in vector-like theories
• Extended Supersymmetries and the Dirac Operator
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D
• The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
• Gauging 1-form center symmetries in simple $SU(N)$ gauge theories
• Emergent discrete 3-form symmetry and domain walls
• Deconfinement on axion domain walls
• A possible phase for adjoint QCD
• Bose-Fermi cancellations without supersymmetry
• Self-conjugate QCD
• Low energy properties of SU(2) gauge theory with N_f = 3/2 flavours of adjoint fermions
• Explorations of Compositeness

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• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
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