QCD as a topologically ordered system

TL;DR

This paper proposes that QCD exhibits topological order similar to condensed matter systems, using deformed QCD to analyze topological features, and connects these to the resolution of the $U(1)_A$ problem and lattice configurations.

Contribution

It introduces a topological BF action for deformed QCD, linking topological order concepts to QCD phenomena and the $U(1)_A$ problem resolution.

Findings

QCD has topological order akin to condensed matter systems.

The BF action reproduces infrared features like topological susceptibility.

The $U(1)_A$ problem is explained via topological field mixing.

Abstract

We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called "deformed QCD" which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial $\theta$ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological "BF" action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which can not be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated $U(1)_A$ problem where the would be $\eta'$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the $U(1)_A$ problem). Finally, we elaborate on relation between "string -net" condensation in topologically ordered condensed matter systems and long range coherent configurations, the "skeletons", studied in QCD lattice simulations.