Vorticity-induced effects from Wess-Zumino-Witten terms

TL;DR

This paper explores how vorticity influences Nambu-Goldstone modes through Wess-Zumino-Witten terms, deriving new vorticity-induced effects in the presence of electromagnetic fields and chemical potentials with potential phenomenological relevance.

Contribution

It provides an alternative derivation of Wess-Zumino-Witten terms and introduces a novel approach to incorporate vorticity as an axial-vector field affecting Nambu-Goldstone modes.

Findings

Derived vorticity-induced current and effects on Nambu-Goldstone modes.

Identified vorticity-modified photon-pion coupling.

Discussed phenomenological implications of vorticity effects.

Abstract

We study vorticity-induced effects arising from the Wess-Zumino-Witten terms for Nambu-Goldstone modes in chiral perturbation theory. We first provide an alternative derivation of the Wess-Zumino-Witten terms in the presence of external vector, axial-vector, and pseudoscalar fields using a derivative expansion of the fermion determinant. We then employ the previously found correspondence in which vorticity is treated as an axial-vector field coupled to Dirac fermions in flat spacetime. Using this, we derive vorticity-induced contributions for Nambu-Goldstone modes in the presence of electromagnetic fields at finite baryon and isospin chemical potentials, including a vorticity-induced current, a magnetic-field-induced angular momentum, and a vorticity-modified photon-pion coupling. We also briefly discuss the phenomenological implications of these vorticity-induced effects.