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

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 quar...

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Authors: Catillo, Marco, Leonid Ya Glozman, Lang, Christian B
Format: Article
Language:English
Subjects:
Baryons
Correlators
Emergence
Flavor (particle physics)
Hadrons
Lattice vibration
Quarks
Subgroups
Symmetry
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.01969