Extracting topological information from momentum space propagators

Abstract

A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.

arXiv comment18 pages, 2 figures. Comments added and relevant references included

References in corpus (42)

• Topological insulators and superconductors
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Stability of Fermi Surfaces and K-Theory
• Analytic properties of the Landau gauge gluon and quark propagators
• Quantum phase transitions from topology in momentum space
• Unquenched quark propagator in Landau gauge
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• Confinement and complex singularities in QED3
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Self-tuning vacuum variable and cosmological constant
• Positivity violation for the lattice Landau gluon propagator
• Spectral functions of confined particles
• Chiral symmetry breaking with lattice propagators
• Reconstructing the gluon
• Källén-Lehmann spectroscopy for (un)physical degrees of freedom
• Locating the Gribov horizon
• On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations
• Two-point correlation functions of QCD in the Landau gauge
• Landau gauge gluon and ghost propagators at finite temperature from quenched lattice QCD
• High Precision Statistical Landau Gauge Lattice Gluon Propagator Computation vs. the Gribov-Zwanziger approach
• Analytic structure of QCD propagators in Minkowski space
• Quark propagator with two flavors of O(a)-improved Wilson fermions
• Nontrivial ghost-gluon vertex and the match of RGZ, DSE and lattice Yang-Mills propagators
• Topological invariants for Standard Model: from semi-metal to topological insulator
• Unqueched Kogut-Susskind quark propagator in Lattice Landau Gauge QCD
• Spectral representation of lattice gluon and ghost propagators at zero temperature
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• z=3 Lifshitz-Horava model and Fermi-point scenario of emergent gravity
• Bayesian analysis of quark spectral properties from the Dyson-Schwinger equation
• Complex poles and spectral function of Yang-Mills theory
• Running mass, effective energy and confinement: the lattice quark propagator in Coulomb gauge
• Finite temperature gluon spectral functions from $N_f=2+1+1$ lattice QCD
• Momentum space topological invariants for the 4D relativistic vacua with mass gap
• Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement
• Non-perturbative constraints on the quark and ghost propagators
• Standard Model as the topological material
• Topology of quantum vacuum