Self-Intersection, Axial Anomaly and the String Picture of QCD

TL;DR

This paper explores a string-theoretic model of QCD where quarks are confined to the boundary of a world surface, linking topological invariants like self-intersection number to QCD theta-vacua.

Contribution

It introduces a novel approach to model quark confinement and theta-vacua in QCD using boundary conditions and topological invariants within a string framework.

Findings

Quarks confined to the boundary via infinite mass interior

QCD theta-vacua represented by self-intersection number

Connection between topological invariants and QCD vacua

Abstract

The leading, planar diagrams of the $1/N_c$ expansion and the usual string description suggest that quarks propagate on the boundary of a two-dimensional world surface. We restrict the quarks to the boundary of the world surface by giving them infinitely large mass on the interior of the surface and zero mass on its boundary and show that in this picture the QCD $\theta$--vacua can be represented by the self-intersection number (or equivalently by the first Chern number of the normal bundle) of the surface.