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arXiv · 1904.01969

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

Marco Catillo·Leonid Ya. Glozman·Christian B. Lang
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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.

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Marco Catillo, Leonid Ya. Glozman, Christian B. Lang. 2019-04-03. Chiral-spin symmetry emergence in baryons and eigenmodes of the Dirac operator. https://doi.org/10.1103/physrevd.99.094040

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