Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD

Abstract

We show that there exists a special compactification of QCD on ${\mathbb{R}}^3\times S^1$ in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation $m_{\pi }^2{f}_{\pi }^2=m_q⟨\bar{q}q⟩$. Abelian duality, monopole operators, and flavor-twisted boundary conditions, or a background flavor holonomy, play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole-instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons". We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large $S^1$, and yield strong support for adiabatic continuity between the small-$S^1$ and large-$S^1$ regimes. We also find concrete microscopic connections between $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric gauge theory dynamics and non-supersymmetric QCD dynamics.

v1: 6 pages, 2 figures

References in corpus (14)

• Color superconductivity in dense quark matter
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Conformality or confinement: (IR)relevance of topological excitations
• Finite size phase transitions in QCD with adjoint fermions
• New Phases of SU(3) and SU(4) at Finite Temperature
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion Electromagnetic Form Factor
• Anderson Localization in high temperature QCD: background configuration properties and Dirac eigenmodes

Cited by in corpus (43)

• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Circle compactification and 't Hooft anomaly
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Order parameters and color-flavor center symmetry in QCD
• QCD on a small circle
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• Resurgence in $\eta$-deformed Principal Chiral Models
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Some Exact Results in QCD-like Theories
• Chiral Symmetry Breaking on the Lattice
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• From 3d dualities to hadron physics
• Emergent Dimensions and Braneworlds from Large-N Confinement
• Gradient flows without blow-up for Lefschetz thimbles
• Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• String tensions in deformed Yang-Mills theory
• Bose-Fermi cancellations without supersymmetry
• Vacuum structure of Yang-Mills theory as a function of $\theta$
• The Instanton-Dyon Liquid Model V: Twisted Light Quarks
• Self-conjugate QCD
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• Lattice simulations of a gauge theory with mixed adjoint-fundamental matter
• Twisted Sisters: KK Monopoles and their Zero Modes
• Classification of compactified $su(N_c)$ gauge theories with fermions in all representations
• Exponential reduction of finite volume effects with twisted boundary conditions
• Quantum distillation in QCD
• Sign problem in $Z_3$-symmetric effective Polyakov-line model
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Strongly coupled QFT dynamics via TQFT coupling
• New nonperturbative scales and glueballs in confining supersymmetric gauge theories
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Symmetry Crossover Protecting Chirality in Dirac Spectra
• 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
• Confinement from Correlated Instanton-Dyon Ensemble in SU(2) Yang-Mills Theory
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses
• Quantum Chromodynamics: Computational Aspects