QCD as a topologically ordered system

•QCD may belong to a topologically ordered phase similar to condensed matter (CM) systems.•We identify the non-propagating topological field in deformed QCD with the Veneziano ghost.•Relation between “string-net” condensates in CM systems and the “skeletons” in QCD lattice simulations is studied.

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 θθ 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 cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1)AU(1)A problem where the would be η′η′ 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)AU(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.