Monte Carlo Meets the Fishnet: String Formation in a Gas of Feynman Diagrams
Mar, 198438 pages
Published in:
- Nucl.Phys.B 249 (1985) 263-300
- Published: Jan 21, 1985
Report number:
- NBI-HE-84-10
Citations per year
Abstract: (Elsevier)
It is likely that the quark confinement mechanism at large N should be understood purely in terms of high-order planar Feynman diagrams; in particular, the center of the gauge group can play no role whatever. With this motivation I consider the diagrammatic expansion of loop integrals 〈 P Tr exp(g∫ø)〉 in planar wrong-sign ø 4 theory. It is shown that the sum of all fishnet diagrams contributing to the loop can be expressed as the grand partition function of an unusual gas, whose dynamics can be simulated on a computer. The “molecules” of this gas correspond to vertices of the position-space diagrams, the molecular interactions are determined by the propagators, and the coupling constant plays the role of a chemical potential. The most remarkable feature of this gas is the existence of a critical coupling g c , where string formation takes place. As g → g c the fishnet vertices tend to cluster around the minimal surface of the loop, thereby forming a string. This is clearly illustrated with the help of computer graphics. The role of asymptotic freedom in bringing the coupling to the critical point, and the connection to the Polyakov string, are also discussed. In the hamiltonian formulation a new and very straightforward explanation of quark confinement is presented.- field theory: scalar
- FEYNMAN GRAPH: PLANAR
- MODEL: GAS
- MODEL: STRING
- STATISTICAL MECHANICS: CRITICAL PHENOMENA
- QUARK: CONFINEMENT
- PERTURBATION THEORY: HIGHER-ORDER
- FIELD THEORY: ASYMPTOTIC FREEDOM
- GAUGE FIELD THEORY: WILSON LOOP
- MODEL: FLUX TUBE
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