Chiral Symmetry Breaking

Chiral symmetry breaking is the spontaneous breakdown of chiral symmetry in quantum field theories with massless fermions, most prominently in quantum chromodynamics. In the massless limit, QCD's Lagrangian possesses separate symmetries for left- and right-handed quarks; these are spontaneously broken by the QCD vacuum, which forms a quark condensate that couples the two chiralities. The result is the emergence of pions as Goldstone bosons and the generation of constituent quark masses far larger than the bare Lagrangian masses. On the lattice, this phenomenon is notoriously difficult to capture without explicit chiral symmetry, which makes domain-wall fermions and the overlap operator essential tools.