Chiral-spin symmetry emergence in baryons and eigenmodes of the Dirac operator

Abstract

Truncating the low-lying modes of the lattice Dirac operator results in an emergence of the chiral-spin symmetry $SU(2{)}_{CS}$ and its flavor extension $SU(2N_F)$ in hadrons. These are symmetries of the quark - chromo-electric interaction and include chiral symmetries as subgroups. Hence the quark - chromo-magnetic interaction, which breaks both symmetries, is located at least predominantly in the near - zero modes. Using as a tool the expansion of propagators into eigenmodes of the Dirac operator we here analytically study effects of a gap in the eigenmode spectrum on baryon correlators. We find that both $U(1{)}_A$ and $SU(2{)}_L\times SU(2{)}_R$ emerge automatically if there is a gap around zero. Emergence of larger $SU(2{)}_{CS}$ and $SU(4)$ symmetries requires in addition a microscopical dynamical input about the higher-lying modes and their symmetry structure.

arXiv commentAccepted by PRD

References in corpus (11)

• Evidence of effective axial U(1) symmetry restoration at high temperature QCD
• The High Temperature Phase of QCD and {\boldmath $U(1{)}_A$} Symmetry
• Symmetries of hadrons after unbreaking the chiral symmetry
• Unbreaking chiral symmetry
• Symmetries of mesons after unbreaking of chiral symmetry and their string interpretation
• Isoscalar mesons upon unbreaking of chiral symmetry
• SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra
• Approximate degeneracy of $J=1$ spatial correlators in high temperature QCD
• Chiralspin symmetry and QCD at high temperature
• Baryon parity doublets and chiralspin symmetry
• Low lying eigenmodes and meson propagator symmetries

Cited by in corpus (2)

• Chiral spin symmetry and hot/dense QCD
• Gap in the Dirac spectrum and quark propagator symmetries in lattice QCD