Aspects of Chiral Symmetry and the Lattice

Abstract

I explore the non-perturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, I discuss how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP violating parameter $\Theta$. I then turn to a particularly elegant scheme for exploring this physics on the lattice. This uses an auxiliary extra space-time dimension, with the physical world being a four dimensional interface.

86 pages, 30 figures, replacement adds and corrects a few references

References in corpus (5)

• Lattice regularization of chiral gauge theories to all orders of perturbation theory
• Locality bound for effective four-dimensional action of domain-wall fermion
• Lanczos Approach to the Inverse Square Root of a Large and Sparse Matrix
• Hamiltonian domain wall fermions at strong coupling
• Overlap-Dirac fermions with a small hopping parameter

Cited by in corpus (70)

• Topological Field Theory of Time-Reversal Invariant Insulators
• The Quantum Spin Hall Effect: Theory and Experiment
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Chiral Ladders and the Edges of Chern Insulators
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Four-dimensional graphene and chiral fermions
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Topological circuits of inductors and capacitors
• Magic Fermions: Carroll and Flat Bands
• Flat-band many-body localization and ergodicity breaking in the Creutz ladder
• Localization in Lattice QCD
• Torsion, Parity-odd Response and Anomalies in Topological States
• Spontaneous violation of CP symmetry in the strong interactions
• Patterns of Electro-magnetic Response in Topological Semi-metals
• An Introduction to Chiral Symmetry on the Lattice
• Finite-size effects in non-Hermitian topological systems
• One-dimensional $2^n$-root topological insulators and superconductors
• Strong-Field Physics in QED and QCD: From Fundamentals to Applications
• Ambiguities in the up quark mass
• Quantum Charge Pumps with Topological Phases in Creutz Ladder
• Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence
• Exact holographic mapping in free fermion systems
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Exact Chiral Symmetry on the Lattice
• Phase-induced topological superconductivity in a planar heterostructure
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice
• D-branes in Massive IIA and Solitons in Chern-Simons Theory
• Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure
• Analytic Theory of Edge Modes in Topological Insulators
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Hadron masses in QCD with one quark flavour
• One flavor QCD
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Supersymmetric QCD on the Lattice: An Exploratory Study
• Topological winding properties of spin edge states in Kane-Mele graphene model
• Unconventional Quantum Electrodynamics with Hofstadter-Ladder Waveguide
• Two-loop critical mass for Wilson fermions
• Compactly Supported Wannier Functions and Strictly Local Projectors
• On the renormalization of the bosonized multi-flavor Schwinger model
• Entanglement Entropy & Anomaly Inflow
• Tailoring flat bands and topological phases in a multi-strand Creutz network
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Topological chiral currents in the Gross-Neveu model extension
• Supersymmetric QCD: Renormalization and Mixing of Composite Operators
• CP, T and CPT in the non-perturbative formulation of chiral gauge theories
• Chiral fermions on the lattice
• From Euclidean to Minkowski space with the Cauchy-Riemann equations
• Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band
• Renormalization and Mixing of the Gluino-Glue Operator on the Lattice
• Helical Edge Modes near Transition to Topological Insulator with Indirect Gap
• Yang-Mills fields and the lattice
• The invariant factor of the chiral determinant
• Diseases with rooted staggered quarks
• Cosine Edge Mode in a Periodically Driven Quantum System
• Chiral Magnetic Effect on the Lattice
• In-medium polarization tensor in strong magnetic fields (II): Axial Ward identity at finite temperature and density
• Hidden symmetries in two dimensional field theory
• Chiral Chaos Enhanced Sensing
• Chiral symmetry on the lattice
• The one-flavor quark condensate and related problems
• Local Optical Conductivity of Bilayer Graphene with Kink Potential
• Vacuum Alignment with more Flavors
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Exact Mappings in Condensed Matter Physics
• Topological bound states in a lattice of rings with nearest-neighbour interactions
• Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme