Monte Carlo Meets the Fishnet. String Formation in a Gas of Feynman Diagrams

摘要

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 whatsoever. The author considers the diagrammatic expansion of loop integrals in planar wrong-sign phi4 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 gsub(c), where string formation takes place. As g implies gsub(c) the fishnet vertices tend to cluster around the minimal surface of the loop, thereby forming a string. 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 very straightforward explanation of quark confinement is presented. (Atomindex citation 15:054816)