Kaon Condensation and Goldstone's Theorem

Abstract

We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that, when the isospin symmetry is exact in the Lagrangian, a Goldstone boson with a dispersion relation $E\sim p^2$ appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. Both phenomena are familiar in non-relativistic systems. We interpret our results in terms of a Goldstone boson counting rule found previously by Nielsen and Chadha. We also formulate a criterion sufficient for the equality between the number of Goldstone bosons and the number of broken generators.

13 pages, 1 figure, Latex

References in corpus (15)

• Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD
• QCD at finite isospin density
• On the Foundations of Chiral Perturbation Theory
• QCD-like Theories at Finite Baryon Density
• Inverse meson mass ordering in color-flavor-locking phase of high density QCD
• On two-color QCD with baryon chemical potential
• Nonrelativistic effective Lagrangians
• QCD-like Theories at Finite Baryon and Isospin Density
• Inverse meson mass ordering in color-flavor-locking phase of high density QCD: erratum
• QCD at small non-zero quark chemical potentials
• Kaon Condensation in High Density Quark Matter
• Spin-wave Scattering in the Effective Lagrangian Perspective
• Phonons as Goldstone Bosons
• Zero temperature phase transitions in quantum Heisenberg ferromagnets
• Effective Low Energy Theories and QCD Dirac Spectra

Cited by in corpus (121)

• Color superconductivity in dense quark matter
• NJL-model analysis of dense quark matter
• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• An Introduction to Spontaneous Symmetry Breaking
• Two lectures on color superconductivity
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
• On the number of Nambu-Goldstone bosons and its relation to charge densities
• Redundancies in Nambu-Goldstone Bosons
• Compensating strong coupling with large charge
• Effective Lagrangian for Nonrelativistic Systems
• The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory
• Color Superconductivity at Moderate Baryon Density
• Massive Nambu-Goldstone Bosons
• A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
• Scrutinizing the pion condensed phase
• More on gapped Goldstones at finite density: More gapped Goldstones
• Counting Rules of Nambu-Goldstone Modes
• Thermal conductivity of dense quark matter and cooling of stars
• The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature
• Selected Topics in the Large Quantum Number Expansion
• Anisotropic admixture in color-superconducting quark matter
• Pion and Kaon Condensation at Finite Temperature and Density
• Global Strings in High Density QCD
• Abnormal number of Nambu-Goldstone bosons in the color-asymmetric 2SC phase of an NJL-type model
• Mass Terms in Effective Theories of High Density Quark Matter
• Bogoliubov Theory and Lee-Huang-Yang Corrections in Spin-1 and Spin-2 Bose-Einstein Condensates in the Presence of the Quadratic Zeeman Effect
• Spontaneous breaking of continuous translational invariance
• Superfluidity in a Three-flavor Fermi Gas with SU(3) Symmetry
• Holographic Superfluids and the Landau Criterion
• The QCD phase diagram at nonzero baryon, isospin and strangeness chemical potentials: Results from a hadron resonance gas model
• Bulk viscosity in kaon-condensed color-flavor locked quark matter
• Spontaneous symmetry breaking and Nambu-Goldstone modes in dissipative systems
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• General Structure of Relativistic Vector Condensation
• Pion, sigma-meson and diquarks in the 2SC phase of dense cold quark matter
• Spontaneous Superfluid Current Generation in CFL at Nonzero Strange Quark Mass
• Counting Nambu-Goldstone modes of higher-form global symmetries
• Spontaneous rotational symmetry breaking and roton like excitations in gauged sigma-model at finite density
• Effective field theory for spacetime symmetry breaking
• BCS-BEC crossover in dense relativistic matter: Collective excitations
• Effective Lagrangians for quantum many-body systems
• Remarks on nonrelativistic Goldstone bosons
• Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems
• Spontaneous symmetry breaking and Nambu-Goldstone modes in open classical and quantum systems
• Relativistic Massive Vector Condensation
• Goldstone boson counting in linear sigma models with chemical potential
• Spontaneous symmetry breaking in the linear sigma model at finite chemical potential: One-loop corrections
• Critical temperature for kaon condensation in color-flavor locked quark matter
• Spontaneous Magnetization of an Ideal Ferromagnet: Beyond Dyson's Analysis
• Quasi-Nambu-Goldstone modes in nonrelativistic systems
• Surprises in nonperturbative dynamics in sigma-model at finite density
• Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
• New Bounds on the String Scale from Flavor Physics
• Diquark Bose-Einstein Condensation and Nuclear Matter
• The minimal curvature of the universe in modified gravity and conformal anomaly resolution of the instabilities
• Manifestation of Instabilities in Nambu-Jona-Lasinio type models
• Nambu-Goldstone bosons and the Higgs mechanism without Lorentz invariance: Analysis based on constrained-system theory
• Mass spectrum of diquarks and mesons in the color--flavor locked phase of dense quark matter
• Goldstone bosons in presence of charge density
• Gluonic phases, vector condensates, and exotic hadrons in dense QCD
• Symmetry Realization via a Dynamical Inverse Higgs Mechanism
• Fate of chiral critical point under the strong isospin asymmetry
• Neutrino processes in the $K^0$ condensed phase of color flavor locked quark matter
• Mesons and diquarks in neutral color superconducting quark matter with $\beta$-equilibrium
• Diquarks in the color--flavor locked phase of dense quark matter
• Holographic Type II Goldstone bosons
• 3D two-color QCD at finite temperature and baryon density
• Finite Density Two Color Chiral Perturbation Theory Revisited
• The Nambu-Goldstone theorem in non-relativistic systems
• Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet
• A Note on Holographic Non-Relativistic Goldstone Bosons
• Chiral Perturbation Theory in a Nuclear Background
• Dynamical stabilization of runaway potentials at finite density
• Kaon condensation in the color-flavor-locked phase of quark matter, the Goldstone theorem, and the 2PI Hartree approximation
• Englert-Brout-Higgs Mechanism in Nonrelativistic Systems
• Field theoretic description of the abelian and non-abelian Josephson effect
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Phonons in Electron Crystals with Berry Curvature
• Higgs Mechanism with Type-II Nambu-Goldstone Bosons at Finite Chemical Potential
• Scattering amplitudes of massive Nambu-Goldstone bosons
• Vortices in gauge models at finite density with vector condensates
• Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism
• Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
• Formation of a supergiant quantum vortex in a relativistic Bose-Einstein condensate driven by rotation and a parallel magnetic field
• Magnon Energy Renormalization and Low-Temperature Thermodynamics of O(3) Heisenberg Ferromagnets
• Fractons in effective field theories for spontaneously broken translations
• Engineering holographic flat fermionic bands
• Effective Theories of Dense and Very Dense Matter
• Anomaly Matching and Low Energy Theories at High Matter Density
• Background field method at finite temperature and density
• Unstable Nambu-Goldstone modes
• Emergence of the Unconventional Type-II Nambu-Goldstone Modes with Topological Origin in Bose Superfluids
• Fractal dimension and the counting rule of the Goldstone modes
• Stability and Absence of a Tower of States in Ferrimagnets
• Random matrix model at nonzero chemical potentials with anomaly effects
• Order from disorder in lattice QCD at high density
• Aspects of the Quantum Chromo Dynamics Phase Diagram
• Is gluonic color-spin locked phase stable?
• Inhomogeneous superfluids
• Meissner screening masses in gluonic phase
• The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory
• Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
• Gapped dilatons in scale invariant superfluids
• Fractals and spontaneous symmetry breaking with type-B Goldstone modes: a perspective from entanglement
• Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids
• Entanglement entropy in low-energy field theories at finite chemical potential
• Phonon spectrum of QCD vacuum in magnetic-field-induced superconducting phase
• Dynamical stabilization of runaway potentials and landscape of vacua at finite density
• How does color neutrality affect collective modes in color superconductors?
• Geometry of Classical Nambu-Goldstone Fields
• How Infrared Singularities Affect Nambu-Goldstone Bosons at Finite Temperatures
• An introduction to Goldstone boson physics and to the coset construction
• Anisotropic Goldstone bosons of strong-coupling lattice QCD at high density
• Relativistic BEC extracted from a complex FRG flow equation
• A study of meson condensation and of the QCD critical line
• Dense baryonic matter in strong coupling lattice gauge theory
• Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model
• Anisotropic QCD superfluids
• Spontaneous symmetry breaking in strong and electroweak interactions
• Renormalisation Group Flow and Kaon Condensation