Chiral symmetry breaking and confinement: separating the scales

Abstract

We review arguments that chiral symmetry breaking is triggered when the quark bilinear condensate's dimension passes through one ($\gamma =1$). This is supported by gap equations and more recently holographic models. Confinement may then be a separate property of the pure Yang-Mills theory below the scale of the dynamically generated quark mass, occurring at the scale of the pole in the deep IR running. Here, we use perturbative results for the running of the gauge coupling and $\gamma$ in asymptotically free SU($N_c$) gauge theories with matter in higher dimension representations to seek the best candidate theories where confinement and chiral symmetry breaking can be maximally separated. For example, SU(2) gauge theory with a single Weyl quark in the $S_3$ (dimension 4) representation may have a factor of 20 separation in scale. Such a theory could be simulated on the lattice to test the separation. We also propose studying multi-representation theories where the higher dimension representation forms a condensate at one scale that can be quite separate from the condensation scale of the second representation matter. The confinement scale would presumably be below the second scale. For example, SU(3) gauge theory with a Weyl adjoint fermion and ten fundamental quarks may have a separation of a factor of 20 also.

arXiv comment9 pages, 2 figures, 1 table, v2: added commentary, v3: minor corrections, added references

References in corpus (48)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The QCD transition temperature: results with physical masses in the continuum limit
• Phases of Dense Quarks at Large N_c
• Chiral Symmetry Breaking and Pions in Non-Supersymmetric Gauge/Gravity Duals
• Lattice Study of the Conformal Window in QCD-like Theories
• Fermionic UV completions of Composite Higgs models
• The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories
• Higher representations on the lattice: numerical simulations. SU(2) with adjoint fermions
• Holographic Models for QCD in the Veneziano Limit
• Supersymmetry Inspired QCD Beta Function
• AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields
• Confinement versus Chiral Symmetry
• Deconfinement and Chiral Symmetry Restoration in an SU(3) Gauge Theory with Adjoint Fermions
• Flavoured Large N Gauge Theory in an External Magnetic Field
• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
• Infrared fixed point in SU(2) gauge theory with adjoint fermions
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• Determining the conformal window: SU(2) gauge theory with N_f = 4, 6 and 10 fermion flavours
• The infrared regime of SU(2) with one adjoint Dirac flavour
• Thermodynamics of lattice QCD with 2 flavours of colour-sextet quarks: A model of walking/conformal Technicolor
• Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
• Conformal Phase Transitions at Weak and Strong Coupling
• Deconfined, Massive Quark Phase at High Density and Compact Stars: A Holographic Study
• Unbreaking chiral symmetry
• Improving the continuum limit of gradient flow step scaling
• Minimal Composite Inflation
• Dynamic AdS/QCD and the Spectrum of Walking Gauge Theories
• Holography of the Conformal Window
• Relation between chiral symmetry breaking and confinement in YM-theories
• Finite-temperature phase structure of SU(4) gauge theory with multiple fermion representations
• Holographic quark matter with colour superconductivity and a stiff equation of state for compact stars
• Near the sill of the conformal window: gauge theories with fermions in two-index representations
• Separation of Spontaneous Chiral Symmetry Breaking and Confinement via AdS/CFT Correspondence
• Running coupling in SU(2) gauge theory with two adjoint fermions
• Phase structure of the N=1 supersymmetric Yang-Mills theory at finite temperature
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• Running coupling in the conformal window of large-Nf QCD
• Relating Quark Confinement and Chiral Symmetry Breaking in QCD
• Lattice simulations of a gauge theory with mixed adjoint-fundamental matter
• Confinement and Chiral Symmetry
• Low energy properties of SU(2) gauge theory with N_f = 3/2 flavours of adjoint fermions
• Monte-Carlo simulations of overlap Majorana fermions
• The chiral phase transition for lattice QCD with 2 colour-sextet quarks
• Separating the scales of confinement and chiral-symmetry breaking in lattice QCD with fundamental quarks
• SU(3) sextet model with Wilson fermions

Cited by in corpus (8)

• Holographic modeling of nuclear matter and neutron stars
• Dark Confinement and Chiral Phase Transitions: Gravitational Waves vs Matter Representations
• Neutron stars and phase diagram in a hard-wall AdS/QCD model
• Investigating the conformal behaviour of SU(2) with one adjoint Dirac flavor
• Correlations between the deconfining and chiral transitions in holographic QCD
• Holography for Sp(2$N_c$) Gauge Dynamics: from Composite Higgs to Technicolour
• Holography of Strongly Coupled Gauge Theories
• SU(2) gauge theory with one and two adjoint fermions towards the continuum limit