On SU(2)CS-like groups and invariance of the fermionic action in QCD

Abstract

In this work, we introduce some new U(1) symmetry groups of the free fermionic action in Euclidean space–time, which are a consequence of parity and time-reversal symmetries. Afterwards, we discuss how the introduction of a gauge interaction affects the invariance of the action, with special reference to QCD. Moreover, inspired by recent QCD lattice results of Glozman et al., in which an interesting and unexpected symmetry group has been observed, namely [Formula: see text] (that contains [Formula: see text] as subgroup), we build other [Formula: see text]-like groups in Euclidean space–time using the previously introduced U(1) groups. Finally we argue about the possible invariance of the fermionic action with respect these new [Formula: see text]-like groups and its consequence on the hadron temporal correlators.