Quark-hadron duality in hydrodynamics: an example

TL;DR

This paper explores how quark-hadron duality links the polarization of hyperons in rotating quark-gluon plasma to vortex structures, using a pionic superfluidity model to connect field theory anomalies with hydrodynamic vorticity.

Contribution

It demonstrates the duality between anomalous triangle diagrams in effective field theory and vorticity terms in hydrodynamics, fixing polarization coefficients through fundamental theory.

Findings

Vortices in superfluid models correspond to baryon spins.

Duality relates triangle anomalies to hydrodynamic vorticity.

Polarization coefficients are determined by fundamental field theory.

Abstract

We consider the problem of transferring overall rotation of quark-gluon plasma to polarization of hyperons along the rotation axis. As a toy theoretical model, we exploit that of pionic superfluidity induced by chemical potentials violating isotopic symmetry. Apparently, the model accounts only for the light degrees of freedom, that is pions. The rotation, however, results in vortices which are infinitely thin in the hydrodynamic approximation. Field theory resolves the singularity and predicts that the core of the vortices is build up on spins of baryons. We review consequences from the quark-hadron duality in this case. First, an anomalous triangle graph in effective field theory turns to be dual to the vorticity term in the standard hydrodynamic expansion. And, then, the overall coefficient determining the polarization of baryons is fixed by duality with the triangle graph in the fundamental field theory.