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

## TL;DR

This paper investigates how truncating low-lying Dirac eigenmodes in lattice QCD reveals emergent chiral-spin symmetries in baryons, highlighting the role of eigenmode gaps and higher modes in symmetry formation.

## Contribution

It analytically studies the impact of eigenmode spectrum gaps on baryon correlators and the emergence of chiral-spin symmetries in QCD.

## Key findings

- Emergence of $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries with a gap around zero eigenmodes.
- Chiral-spin $SU(2)_{CS}$ and $SU(4)$ symmetries require additional microscopic input.
- Eigenmode truncation isolates quark-chromo-electric interactions, revealing hidden symmetries.

## 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.