$SU(4)$-Ward identities for QCD with restored chiral symmetry

TL;DR

This paper derives $SU(4)$ Ward identities in continuum QCD, revealing conditions under which approximate $SU(4)$ symmetry emerges in hadron spectra at high temperatures, despite the classical action not being invariant.

Contribution

It provides a derivation of $SU(4)$ Ward identities in the continuum limit and analyzes their implications for chiral symmetry restoration in QCD.

Findings

$SU(4)$ Ward identities simplify with a gap in low-lying Dirac modes.

Approximate $SU(4)$ symmetry can emerge in high-temperature quark matter.

Implications for hadron spectra and chiral symmetry restoration are discussed.

Abstract

Lattice studies of QCD at temperatures above the chiral restoration and QCD with truncated low modes of the Dirac operator indicate approximate and explicit $SU(4)$ degeneracies in hadron spectra, respectively. At the same time, the QCD classical action and the path integral measure are not invariant under $SU(4)$. Here we investigate $SU(4)$ transformations in the continuum limit by deriving corresponding Ward identities. We show that, if there is a gap in low-lying modes of the Dirac operator the obtained $SU(4)$ Ward identities are simplified and look like they would be if $SU(4)$ symmetry is preserved. Then, we discuss possible consequences for the quark matter at high temperatures.