General Motivation

1 Topology

• General Features of QCD Topology

  • • Toy example: particle on a ring

    • Topological charge in gauge theories (SU(2) example)

    • Index theorem

    • Introduction of θ-angle, basics of θ-dependence, strong-CP violation

• Topology on the Lattice

  • • Topology on the lattice: gluonic definition

    • Topology on the lattice: fermionic definition and lattice index theorem

    • Renormalization of the lattice topological charge (overlaps with “Improvement & Renormalization” section)

    • Lattice topology and lattice chirality

• Topology-related Algorithmic Issues

  • • Smoothing algorithms (overlaps with “Algorithms” section)

    • Topological critical slowing down (overlaps with “Algorithms” and “Critical Phenomena” sections) 

    • Rare topological fluctuations (overlaps with “Algorithms” section)

• Topology and Phenomenology

  • • Topology at large-Nc , Witten–Veneziano & U(1)A anomaly (overlaps with “Hadron Physics” section)

    • Topology at finite temperature, DIGA & axions (overlaps with ‘Thermodynamics” and “BSM” s)
      

2 Confinement

• Confinement

  • • General Introduction on the Confinement Problem

    • Interquark potential and string tension

    • Wilson loop and area law

    • Correlators and spectrum of the theory (overlaps with “Hadron Physics” section)

    • Polyakov loop and realization of center symmetry on the lattice

    • Flux tubes & effective strings

    • Green’s functions & confinement scenarios

• FlavorSymmetriesandLow-LyingSpectrum

  • • Flavor symmetries and their fate at the quantum level 

    • Pion mass & the chiral condensate (overlaps with “EFTs” section) 

    • Realization of chiral symmetry on the lattice

    • Large-Nc limit & U(1)A anomaly 

    • Basic introduction on the properties of the glueball spectrum (large-Nc analysis) (overlaps with “Hadron Physics” and “BSM”)

Level legend: •= Beginner, •= Intermediate, •= Advanced