Topological charge membranes and Goldstone boson propagation in QCD

TL;DR

This paper proposes that the QCD vacuum is structured as a laminated array of membranes acting as domain walls, facilitating Goldstone boson propagation through a polarization mechanism linked to topological charge and gauge invariance.

Contribution

It introduces a novel topological membrane model of the QCD vacuum, connecting domain wall structures with Goldstone boson dynamics and gauge invariance constraints.

Findings

QCD vacuum consists of laminated topological membranes.

Goldstone boson propagation is explained via membrane polarization.

Gauge invariance enforces anomaly inflow between bulk and surface currents.

Abstract

Both theoretical arguments and Monte Carlo observations indicate that the topological structure of the QCD vacuum consists of a laminated array of extended, coherent codimension-one membranes of alternating sign. Large-$N_c$ arguments, supported by gauge/string holography, indicate that these membranes are domain walls which separate discrete "flux vacua" with values of the topological $\theta$ parameter which differ by $\pm 2\pi$. This exposes a close analogy with 2D U(1) gauge theory, where $\theta$ can be interpreted as electric polarization, and the domain walls are pointlike charged particles. In 4D QCD, the $\theta$ parameter represents background Ramond-Ramond flux, which can be interpreted as a polarization of the charged membranes in the vacuum. In this framework, the chiral condensate is formed from the quark surface modes on the membranes. Massless Goldstone boson propagation takes place due to a coordination between bulk oscillations of the polarization field $\theta$ and the surface currents represented by the Chern-Simons 3-form on the brane surface. This coordination is enforced by overall gauge invariance which imposes an anomaly inflow constraint between bulk and surface currents.