2001/02/18 by Chris Austin, Austin, Chris
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.hep-th/0102107
openalex publication_date 2001/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The coefficients in the 1/N expansions of the vacuum expectation values and\ncorrelation functions of Wilson loops, in continuum SU(N) gauge theories in 3+1\ndimensions, are shown to be determined by a closed and complete set of\nequations, called the Group-Variation Equations, that exhibit a simple and\nrobust mechanism for the emergence of massive glueballs and the Wilson area\nlaw. The equations predict that the cylinder-topology minimal-area spanning\nsurface term in the two-glueball correlation function, when it exists, must be\nmultiplied by a pre-exponential factor, which for large area A of the\nminimal-area cylinder-topology surface, decreases with increasing A at least as\nfast as 1/\ln(\σ A). If this factor decreases faster than 1/\ln(\σ\nA), then the mass m0++ of the lightest glueball, and the coefficient\n\σ of the area in the Wilson area law, are determined in a precisely\nparallel manner, and the equations give a zeroth-order estimate of\nm0++/\√(\σ) of 2.38, about 33% less than the best lattice value,\nwithout the need for a full calculation of any of the terms in the right-hand\nsides. The large distance behaviour of the vacuum expectation values and\ncorrelation functions is completely determined by terms called island diagrams,\nthe dominant contributions to which come from islands of \fixed size of\nabout 1/\√(\σ). The value of \σ is determined by the point at\nwhich |\β(g)/g| reaches a critical value, and since the large distance\nbehaviour of all physical quantities is determined by islands of the fixed size\n1/\√(\σ), the running coupling g2 never increases beyond the value\nat which |\β(g)/g| reaches the critical value.\n