A chiralspin symmetry in QCD in Minkowski space-time

TL;DR

This paper introduces a new chiralspin symmetry in Minkowski space-time for massless fermions, demonstrating its invariance properties and exploring its potential relevance in high-temperature QCD and non-zero chemical potential scenarios.

Contribution

The paper constructs a novel chiralspin group transformation in Minkowski space-time and proves its invariance properties for free massless fermionic actions and Hamiltonians.

Findings

Invariance of free massless fermionic action under the new chiralspin group.

Invariance of the free massless fermion Hamiltonian under the transformation.

Discussion of potential symmetry presence in high-temperature QCD and at non-zero chemical potential.

Abstract

In this paper, we look how to construct in Minkowski space-time a new type of \textit{chiralspin} group transformation of the spinor fields, similar to the one discovered by recent works of \textit{Glozman et al.} in the context of high temperature QCD and truncated studies in lattice calculations. Afterwards, we prove the invariance of free massless fermionic action under such group transformations, as well the invariance of the Hamiltonian of free massless fermions. At the end, the possible presence of a symmetry driven by such new \textit{chiralspin} group at high temperature QCD, also at non zero chemical potential, is discussed.