QCD as topologically ordered system    [PDF]

Ariel R. Zhitnitsky
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 analysis of the so-called deformed QCD" which is a weakly coupled gauge theory, but nevertheless preserves all 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 when 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 identify the non-propagating auxiliary topological field in 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.
View original: http://arxiv.org/abs/1301.7072