QCD as a topologically ordered system

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 ${\eta }^{\prime }$ 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.

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References in corpus (9)

• Charge separation induced by P-odd bubbles in QCD matter
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Thermal Hadronization and Hawking-Unruh Radiation in QCD
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• Phase Transitions, theta Behavior and Instantons in QCD and its Holographic Model
• Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold
• The Partonic Nature of Instantons
• P and CP Violation and New Thermalization Scenario in Heavy Ion Collisions
• P odd fluctuations and Long Range Order in Heavy Ion Collisions. Deformed QCD as a Toy Model

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