Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions

Abstract

In recent work, we derived the long-distance confining dynamics of certain QCD-like gauge theories formulated on small $S^1\times {\mathbb{R}}^3$ based on symmetries, an index theorem, and Abelian duality. Here, we give the microscopic derivation. The solution reveals a new mechanism of confinement in QCD(adj) in the regime where we have control over both perturbative and nonperturbative aspects. In particular, consider SU(2) QCD(adj) theory with $1\le n_f\le 4$ Majorana fermions, a theory which undergoes gauge symmetry breaking at small $S^1$. If the magnetic charge of the BPS monopole is normalized to unity, we show that confinement occurs due to condensation of objects with magnetic charge 2, not 1. Because of index theorems, we know that such an object cannot be a two identical monopole configuration. Its net topological charge must vanish, and hence it must be topologically indistinguishable from the perturbative vacuum. We construct such non-self-dual topological excitations, the magnetically charged, topologically null molecules of a BPS monopole and $\overline{\mathrm{KK}}$ antimonopole, which we refer to as magnetic bions. An immediate puzzle with this proposal is the apparent Coulomb repulsion between the BPS-$\overline{\mathrm{KK}}$ pair. An attraction which overcomes the Coulomb repulsion between the two is induced by $2n_f$-fermion exchange. Bion condensation is also the mechanism of confinement in $\mathbb{N}=1$ SYM on the same four-manifold. The SU(N) generalization hints a possible hidden integrability behind nonsupersymmetric QCD of affine Toda type, and allows us to analytically compute the mass gap in the gauge sector. We currently do not know the extension to ${\mathbb{R}}^4$.

35 pages, 3 figures, corrected typos, published version

References in corpus (29)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Instantons in QCD
• Born-Infeld particles and Dirichlet p-branes
• Periodic Instantons with non-trivial Holonomy
• SU(2) Calorons and Magnetic Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Monopole Constituents inside SU(n) Calorons
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators
• Quantum Solitons in Affine Toda Field Theories
• Confinement and Strings in MQCD
• Monopoles and Instantons on Partially Compactified D-Branes
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• TASI Lectures on Solitons
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Deconfinement and Chiral Symmetry Restoration in an SU(3) Gauge Theory with Adjoint Fermions
• Colour confinement and dual superconductivity of the vacuum - I
• Geometric Engineering of N=1 Quantum Field Theories
• Monopoles, affine algebras and the gluino condensate
• Conformality or confinement: (IR)relevance of topological excitations
• (In)validity of large N orientifold equivalence
• Confining ensemble of dyons
• New Phases of SU(3) and SU(4) at Finite Temperature
• Topological objects in QCD
• Confinement for all values of the coupling in four-dimensional SU(2) gauge theory
• Confining Effective Theories Based on Instantons and Merons
• BPS Z(N) String Tensions, Sine Law and Casimir Scaling and Integrable Field Theories

Cited by in corpus (171)

• Physics of Strongly coupled Quark-Gluon Plasma
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• A semiclassical realization of infrared renormalons
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• 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
• Conformality or confinement: (IR)relevance of topological excitations
• Modified instanton sum in QCD and higher-groups
• Finite size phase transitions in QCD with adjoint fermions
• Theta dependence, sign problems and topological interference
• Effective matrix model for deconfinement in pure gauge theories
• Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Complexified path integrals, exact saddles and supersymmetry
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Hidden topological angles and Lefschetz thimbles
• Two-flavor adjoint QCD
• Global symmetries, volume independence and continuity
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• 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
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Confining Dyon-Anti-Dyon Coulomb Liquid Model I
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Light Quarks in the Screened Dyon-Anti-Dyon Coulomb Liquid Model II
• Large-N reduction in QCD-like theories with massive adjoint fermions
• QCD on a small circle
• Confinement in Anti-de Sitter Space
• 2d affine XY-spin model/ 4d gauge theory duality and deconfinement
• Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• Anderson localization through Polyakov loops: lattice evidence and Random matrix model
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Conformality or confinement (II): One-flavor CFTs and mixed-representation QCD
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Double-winding Wilson loops and monopole confinement mechanisms
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Chiral gauge dynamics and dynamical supersymmetry breaking
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Instanton-dyon Ensemble with two Dynamical Quarks: the Chiral Symmetry Breaking
• Near the sill of the conformal window: gauge theories with fermions in two-index representations
• Relations among topological solitons
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum
• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
• Vacuum Structure of Charge k Two-Dimensional QED and Dynamics of an Anti D-String Near an O1- plane
• Theta dependence of the deconfining phase transition in pure SU(N_c) Yang-Mills theories
• Collisional energy loss above the critical temperature in QCD
• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Patterns of Symmetry Breaking in Chiral "QCD"
• Generalized 't Hooft anomalies on non-spin manifolds
• String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories
• Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies
• From 3d dualities to hadron physics
• Instanton Partons in 5-dim SU(N) Gauge Theory
• Deconfinement on axion domain walls
• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms
• Emergent Dimensions and Braneworlds from Large-N Confinement
• Semiclassics with 't Hooft flux background for QCD with $2$-index quarks
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• The Myriad Uses of Instantons
• Phases of Gauge Theories
• Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• $\theta$-dependence and center symmetry in Yang-Mills theories
• A possible phase for adjoint QCD
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
• String tensions in deformed Yang-Mills theory
• Neutral bions in the CP^{N-1} model for resurgence
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• Vacuum structure of Yang-Mills theory as a function of $\theta$
• Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
• Bose-Fermi cancellations without supersymmetry
• The Instanton-Dyon Liquid Model V: Twisted Light Quarks
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Condensates and anomaly cascade in vector-like theories
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• Confinement in Yang--Mills: Elements of a Big Picture
• The Instanton-Dyon Liquid Model III: Finite Chemical Potential
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• Twisted Sisters: KK Monopoles and their Zero Modes
• Semiclassical analysis of the bifundamental QCD on ${\mathbb{R}}^2\times T^2$ with 't Hooft flux
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• Anomalies and phases of strongly-coupled chiral gauge theories: recent developments
• Investigating the conformal behaviour of SU(2) with one adjoint Dirac flavor
• The abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model
• A Chiral SU(N) Gauge Theory Planar Equivalent to Super-Yang-Mills
• Demonstration of Confinement and Chiral Symmetry Breaking in $SO(N_c)$ Gauge Theories
• Gauge theory geography: charting a path between semiclassical islands
• Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
• On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• On the representation (in)dependence of $k$-strings in pure Yang-Mills theory via supersymmetry
• Entanglement entropy, dualities, and deconfinement in gauge theories
• Identification of perturbative ambiguity canceled against bion
• Global Symmetries and Partial Confinement
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence
• New nonperturbative scales and glueballs in confining supersymmetric gauge theories
• Strongly coupled QFT dynamics via TQFT coupling
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Confinement in a Higgs Model on $R^3\times S^1$
• Spectrum of Trace Deformed Yang-Mills Theories
• Conformal windows of SP(2N) and SO(N) gauge theories from topological excitations on R3 * S1
• Phases of circle-compactified QCD with adjoint fermions at finite density
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• Dense Instanton-Dyon Liquid Model: Diagrammatics
• New and Old about Renormalons: in Memoriam Kolya Uraltsev
• Exotic phases of finite temperature SU(N) gauge theories with massive fermions: F, Adj, A/S
• Symmetry Crossover Protecting Chirality in Dirac Spectra
• Cluster expansion and resurgence in Polyakov model
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• Winding theta and destructive interference of instantons
• Monopole-vortex continuity of $\mathcal{N}=1$ super Yang-Mills theory on ${\mathbb{R}}^2\times S^1\times S^1$ with 't Hooft twist
• Musings on the Current Status of HEP
• Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity
• SQCD, Superconducting Gaps and Cyclic RG Flows
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Topological terms and anomaly matching in effective field theories on ${\mathbb{R}}^3\times S^1$: I. Abelian symmetries and intermediate scales
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• High Temperature Confinement in SU(N) Gauge Theories
• Monopoles in Dirac spin liquids and their symmetries from instanton calculus
• Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• Exact WKB in all sectors I: Potentials with degenerate saddles
• Two types of domain walls in $\mathcal{N}=1$ super-QCD: how they are classified and counted
• Deconfinement on ${\mathbb{R}}^2\times S_L^1\times S_{\beta }^1$ for all gauge groups and duality to double Coulomb Gas
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
• Yang-Mills at Strong vs. Weak Coupling: Renormalons, OPE And All That
• Exact-WKB Analysis of Two-level Floquet Systems
• Degenerate Domain Walls in Supersymmetric Theories
• A saddle-point finder and its application to the spin foam model
• Deconfinement transition at weak coupling in Yang-Mills theory on a torus
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory
• SU(2) gauge theory with one and two adjoint fermions towards the continuum limit
• Exact WKB in all sectors II: Potentials with non-degenerate saddles
• High temperature quark localization by Polyakov loops
• Roundtable: What can we learn about confinement and anomalous effects in QCD using analog systems?
• On the perturbative aspects of deformed Yang-Mills theory