Suggested topics/papers

Introduction/overview of widely used lattice discretizations

• Wilson fermions and chiral symmetry (Secs. 5.2 and aspects from 7.1 to 7.3 in Gattringer, Lang) basic
• Staggered fermions (Sec. 10.1 in Gattringer, Lang and further literature) intermediate
• Overlap fermions (Lecture Notes) intermediate
• Domain wall fermions (further literature) challenging

Introduction/overview of widely used lattice methods

• Scale setting basic
• Chiral perturbation theory (Lecture Notes, More Lecture Notes and ref 46-49 of Gattringer) intermediate
• Schroedinger functional intermediate
• Large N volume reduction intermediate
• Topology and the topological freezing problem intermediate
  • Basic reference (topology on the lattice, critical slowing-down; definition of autocorrelation times)
  • More advanced reference (solutions: open BC, non-orientable manifolds)

Introduction/overview of widely used MC algorithms, smoothing and data analysis techniques

• Ulli Wolff method for error analysis basic
• HMC algorithm (Secs. 8.1 and 8.2 in Gattringer, Lang) basic
• RHMC algorithm
• Wilson flow intermediate
  • Basic reference
  • Perturbative analysis
  • Applications ( and a more recent overview)

Further topics

• Chiral spin symmetry basic
• The large N phase diagram intermediate
• Chemical potential on the lattice (introduction from Secs. 12.2-3 in Gattringer) basic
• Isospin chemical potential off and on the lattice intermediate
• Finite density QCD with the canonical ensemble intermediate
• Spectroscopy with Wilson fermions (introduction from Secs. 6.1 to 6.3 in Gattringer, Lang) basic
• Pion spectroscopy with staggered fermions (Tim's Thesis) intermediate
• Confinement and flux tubes (up and including Sec 3.2) intermediate intermediate
• Chiral symmetry restoration with and without anomaly intermediate
• Lattice determination of α_s intermediate
• Renormalization group intermediate
• The chiral magnetic effect intermediate
• Tensor networks challenging