Quark Spin and the Theta-Term for the QCD String

TL;DR

This paper explores how quark spin can be incorporated into a consistent QCD string framework, linking the spin factor to the self-intersection number of 2D surfaces and relating it to the topological charge in QCD.

Contribution

It introduces a novel connection between quark spin, surface self-intersection, and topological charge within the QCD string theory.

Findings

Self-intersection number relates to the topological charge $F\tilde{F}$.

Spin factor of massless fermions linked to surface self-intersection.

Provides a consistent way to include quark spin in QCD string models.

Abstract

We describe a way in which spin of quarks can enter a consistent QCD string theory. We show that the spin factor of the 4d massless, spin 1/2 fermions is related to the self-intersection number of a 2d surfaces immersed in the 4d space. We argue that the latter quantity should appear in a consistent description of the QCD string. We also calculate the chiral anomaly and show that the self-intersection number corresponds to the topological charge $F{\tilde F}$ of QCD.