Anomaly Inflow and Membranes in QCD Vacuum

TL;DR

This paper investigates the membrane-like structures in the QCD vacuum, their relation to topological charge, and how anomaly inflow mechanisms involving Chern-Simons actions could provide insights into confinement and chiral symmetry breaking.

Contribution

It introduces a membrane-based model of the QCD vacuum with anomaly inflow dynamics, linking topological structures to confinement and axial anomalies.

Findings

Membranes localize quark zero modes and topological charge fluctuations.

Coupling of membrane fluctuations to Chern-Simons current explains anomaly inflow.

Long-range Chern-Simons currents may contribute to solving confinement problem.

Abstract

We study the membrane-like structure of topological charge density and its fluctuations in the QCD vacuum. Quark zero modes are localized on the membranes and the resultant gauge anomaly is cancelled by the gauge variation of a Chern-Simons type effective action in the bulk via the anomaly inflow mechanism. The coupling between brane fluctuations, described by the rotations of its normal vector, and the Chern-Simons current provides the needed anomaly inflow to the membrane. This coupling is also related to the axial U(1) anomaly which can induce brane punctures, and consequently quark-antiquark annihilation across the brane. As the Chern-Simons current has a long-range character, together with membranes it might lead to a solution to the confinement problem.