Condensates and anomaly cascade in vector-like theories

Abstract

We study the bilinear and higher-order fermion condensates in $4$-dimensional $SU(N)$ gauge theories with a single Dirac fermion in a general representation. Augmented with a mixed anomaly between the $0$-form discrete chiral, $1$-form center, and $0$-form baryon number symmetries (BC anomaly), we sort out theories that admit higher-order condensates and vanishing fermion bilinears. Then, the BC anomaly is utilized to prove, in the absence of a topological quantum field theory, that nonvanishing fermion bilinears are inevitable in infrared-gapped theories with $2$-index (anti)symmetric fermions. We also contrast the BC anomaly with the $0$-form anomalies and show that it is the former anomaly that determines the infrared physics; we argue that the BC anomaly lurks deep to the infrared while the $0$-form anomalies are just variations of local terms. We provide evidence of this assertion by studying the BC anomaly in vector-like theories compactified on a small spacial circle. These theories are weakly-coupled, under analytical control, and they admit a dual description in terms of abelian photons that determine the deep infrared dynamics. We show that the dual photons talk directly to the $1$-form center symmetry in order to match the BC anomaly, while the $0$-form anomalies are variations of local terms and are matched by fiat. Finally, we study the fate of the BC anomaly in the compactified theories when they are held at a finite temperature. The effective field theory that describes the low-energy physics is $2$-dimensional. We show that the BC anomaly cascades from $4$ to $2$ dimensions.

arXiv comment29 pages, 2 figures

References in corpus (41)

• Generalized Global Symmetries
• Coupling a QFT to a TQFT and Duality
• Theta, Time Reversal, and Temperature
• 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
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Dijet Cross Sections and Parton Densities in Diffractive DIS at HERA
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Monopoles, affine algebras and the gluino condensate
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Anomaly constraints on deconfinement and chiral phase transition
• Conformality or confinement: (IR)relevance of topological excitations
• Modified instanton sum in QCD and higher-groups
• Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
• 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
• Two-flavor adjoint QCD
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• 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
• Microscopic Structure of Magnetic Bions
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• 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)
• 2d affine XY-spin model/ 4d gauge theory duality and deconfinement
• On the baryon-color-flavor (BCF) anomaly in vector-like theories
• Deconfinement in N=1 super Yang-Mills theory on R^3 x S^1 via dual-Coulomb gas and "affine" XY-model
• Lifetimes of (near) eternal false vacua
• Generalized 't Hooft anomalies on non-spin manifolds
• Deconfinement on axion domain walls
• The SU(3)/Z_3 QCD(adj) deconfinement transition via the gauge theory/"affine" XY-model duality
• Self-conjugate QCD
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• Classification of compactified $su(N_c)$ gauge theories with fermions in all representations
• The abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model
• Entanglement entropy, dualities, and deconfinement in gauge theories
• Strongly coupled QFT dynamics via TQFT coupling
• Natural inflation, strong dynamics, and the role of generalized anomalies

Cited by in corpus (6)

• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Semiclassics with 't Hooft flux background for QCD with $2$-index quarks
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Generalized symmetry constraints on deformed 4d (S)CFTs
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles