A Matrix Model for QCD

Abstract

Gribov's observation that global gauge fixing is impossible has led to suggestions that there may be a deep connection between gauge-fixing and confinement. We find an unexpected relation between the topological non-triviality of the gauge bundle and coloured states in $SU(N)$ Yang-Mills theory, and show that such states are necessarily impure. We approximate QCD by a rectangular matrix model that captures the essential topological features of the gauge bundle, and demonstrate the impure nature of coloured states explicitly. Our matrix model also allows the inclusion of the QCD $\theta$-term, as well as to perform explicit computations of low-lying glueball masses. This mass spectrum is gapped. Since an impure state cannot evolve to a pure one by a unitary transformation, our result shows that the solution to the confinement problem in pure QCD is fundamentally quantum information-theoretic.

5 pages LaTex. 3 figures. arXiv admin note: text overlap with arXiv:1407.8352

References in corpus (7)

• Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
• Entanglement and Particle Identity: A Unifying Approach
• Geometry in transition: A model of emergent geometry
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• Matrix Models, Gauge Theory and Emergent Geometry
• Quantum Entropic Ambiguities: Ethylene
• Matrix geometries and Matrix Models

Cited by in corpus (11)

• Glueball Spectra from a Matrix Model of Pure Yang-Mills Theory
• QCD Breaks Lorentz Invariance and Colour
• Quantum Phases of Yang-Mills Matrix Model Coupled to Fundamental Fermions
• Light Hadron Masses from a Matrix Model for QCD
• Maximally Chaotic Dynamical Systems and Fundamental Interactions
• Massless ground state for a compact SU(2) matrix model in 4D
• Born-Oppenheimer Quantization of the Matrix Model for $\mathcal{N}=1$ super-Yang-Mills
• Axial Anomaly in the $SU(N)$ Gauge Matrix Model
• Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions
• Aspects of Boundary Conditions for Nonabelian Gauge Theories
• Emergent Gauge Symmetries and Quantum Operations