Dynamical symmetry breaking in curved spacetime -review-

Abstract

Four-fermion interaction models are considered to be prototype models for dynamical symmetry breaking.The present review deals with recent developments in the studies of dynamical symmetry breaking in the four-fermion interaction models and their extension in curved spacetime. Starting with the Minkowski spacetime in dimension $D$ ($2\le D\le 4$) the effective potential in the leading order of $1/N$-expansion is calculated and the phase structure of the theory is investigated. In curved spacetime curvature-induced phase transitions are discussed in the circumstances where fermion masses are dynamically generated. Subsequently a possibility of curvature- and temperature-induced or curvature- and topology-induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field. Finally some applications of four-fermion models in quantum gravity are briefly described.

88 pages, Latex, epsf.sty, epic.sty and eepic.sty are used

Cited by in corpus (92)

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• Leading Log Solution for Inflationary Yukawa
• Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions
• Analogy between rotation and density for Dirac fermions in a magnetic field
• Universality and the magnetic catalysis of chiral symmetry breaking
• A Maximally Symmetric Vector Propagator
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Cosmological Bardeen-Cooper-Schrieffer condensate as dark energy
• The Influence of an External Chromomagnetic Field on Color Superconductivity
• Fermion Propagator in Cosmological Spaces with Constant Deceleration
• Perturbative confinement in thermal Yang-Mills theories induced by imaginary angular velocity
• The One-Loop Effective Action in phi^4 Theory Coupled Non-Linearly with Curvature Power and Dynamical Origin of Cosmological Constant
• Pion, sigma-meson and diquarks in the 2SC phase of dense cold quark matter
• Unruh effect for interacting particles with ultracold atoms
• Magnetic catalysis of parity breaking in a massive Gross-Neveu model and high-temperature superconductivity
• Fermionic Casimir densities in anti-de Sitter spacetime
• Dynamical Chiral Symmetry Breaking and its Restoration for an Accelerated Observer
• Interacting Fermions, Boundaries, and Finite Size Effects
• Chiral gap effect in curved space
• Pion condensation of quark matter in the static Einstein universe
• A curvature bound from gravitational catalysis
• Dynamical symmetry breaking in the external gravitational and constant magnetic fields
• Cooper pairing and finite-size effects in a NJL-type four-fermion model
• Parameter fitting in three-flavor Nambu--Jona-Lasinio model with various regularizations
• Mesons and diquarks in the color neutral 2SC phase of dense cold quark matter
• $\pi$ and $\sigma$ mesons at finite temperature and density in the NJL model with dimensional regularization
• Dynamical Symmetry Breaking in Spaces with Constant Negative Curvature
• The dual properties of chiral and isospin asymmetric dense quark matter formed of two-color quarks
• Charged pion condensation in dense quark matter: Nambu--Jona-Lasinio model study
• Symmetry Breaking and Lattice Kirigami
• Restoration of Dynamically Broken Chiral and Color Symmetries for an Accelerated Observer
• Inflationary Parameters in Renormalization Group Improved ${\varphi }^4$ Theory
• BCS in the Sky: Signatures of Inflationary Fermion Condensation
• A curvature bound from gravitational catalysis in thermal backgrounds
• Chiral Modulations in Curved Space I: Formalism
• Gravitational instantons and anomalous chiral symmetry breaking
• Gauged Nambu-Jona-Lasinio inflation
• Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
• Chiral Properties of QCD Vacuum in Magnetars- A Nambu-Jona-Lasinio Model with Semi-Classical Approximation
• Influence of chiral asymmetry on phase structure of the two-color quark matter
• Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
• Quark and pion condensation in a chromomagnetic background field
• Generalizing Starobinskii's Formalism to Yukawa Theory & to Scalar QED
• Geometrically induced magnetic catalysis and critical dimensions
• Dynamical Chiral Symmetry Breaking and Superconductivity in the Supersymmetric Nambu$-$Jona-Lasinio Model at finite Temperature and Density
• Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space
• A unified composite model of inflation and dark matter in the Nambu-Jona-Lasinio theory
• The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons
• Temperature induced phase transitions in four fermion models in curved space-time
• Mesons and diquarks in neutral color superconducting quark matter with $\beta$-equilibrium
• Dual Fermion Condensates in Curved Space
• Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Chiral Modulations in Curved Space II: Conifold Geometries
• Finite Density Effect in the Gross-Neveu Model in a Weakly Curved $R^1\times S^2$ Spacetime
• Color superconductivity in the static Einstein Universe
• Chiral Phase Structure at Finite Temperature and Density in Einstein Universe
• Deconfinement transition and Black Holes
• Inflation and dark matter after spontaneous Planck scale generation by hidden chiral symmetry breaking
• Neutron Star Equation of State and the Possibility of Complex Self-Energy in Landau Theory of Fermi Liquid in Presence of Strong Quantizing Magnetic Field
• The Universal One-Loop Effective Action with Gravity
• Finite temperature fermionic condensate in a conical space with a circular boundary and magnetic flux
• Curvature-induced phase transitions in the inflationary universe - Supersymmetric Nambu-Jona-Lasinio Model in de Sitter spacetime -
• On the Crustal Matter of Magnetars
• Color Superconductivity and Radius of Quark Star in Extended NJL Model by Using the Dimensional Regularization
• Precise Phase Structure in Four-fermion Interaction Model on Torus
• Schwinger-Dyson Analysis of Dynamical Symmetry Breaking on a Brane with Bulk Yang-Mills Theory
• NJL model in Four Dimension at Finite Temperature, Chemical Potentialand Curvature
• Dynamical symmetry breaking in the Nambu-Jona-Lasino model with external gravitational and constant electric fields
• Chiral symmetry breaking as a consequence of nontrivial spatial topology
• The Study of Relatively Low Density Stellar Matter in Presence of Strong Quantizing Magnetic Field
• First Order Phase Transitions in a Bianchi type-I universe
• Four-Fermion Interaction Model on ${\mathcal{M}}^{D-1}\otimes S^1$
• Fermionic condensate and the Casimir effect in cosmic string spacetime
• Supersymmetric Nambu$-$Jona-Lasinio Model on $\mathcal{N}=1/2$ four-dimensional Non(anti)commutative Superspace
• Least-Order Torsion-Gravity for Fermion Fields, and the Non-Linear Potentials in the Standard Models
• Casimir effect for fermion condensate in conical rings
• Topological effects in fermion condensate induced by cosmic string and compactification on AdS bulk
• A Gauge-Gravity Relation in the One-loop Effective Action
• Space-time evolution induced by spinor fields with canonical and non-canonical kinetic terms
• Fermionic condensate in de Sitter spacetime
• Vacuum polarization by a scalar field in de Sitter spacetime in the presence of global monopole
• Quantum Monte Carlo simulation with a black hole
• Quantum spinor field in the FRW universe with a constant electromagnetic background
• Derivative four-fermion model, effective action and bumblebee generation
• Topological Casimir effect for fermionic condensate in AdS spacetime with compact dimensions
• Dynamical Chiral Symmetry Breaking, Color Superconductivity, and Bose-Einstein Condensation in an $SU(N_c)\times U(N_f{)}_L\times U(N_f{)}_R$-invariant Supersymmetric Nambu$-$Jona-Lasinio Model
• Fermionic Tachyons as a Source of Dark Energy
• Possibility of Spontaneous Symmetry Breaking in the Nambu-Jona-Lasinio model with torsion
• Radiative Symmetry Breaking and Dynamical Origin of Cosmological Constant in ${\varphi }^4$ Theory with Non-Linear Curvature Coupling
• Fate of chiral symmetry in Riemann-Cartan geometry
• Chiral symmetry and curvature bounds in de Sitter spacetime