Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2001-12-15
Nucl.Phys.Proc.Suppl. 109A (2002) 134-140
Physics
High Energy Physics
High Energy Physics - Lattice
Talk given at LHP2001, Cairns, Australia; 7 pages
Scientific paper
10.1016/S0920-5632(02)01404-4
I show how one can use lattice methods to calculate various continuum properties of SU(N) gauge theories; in part to explore old ideas that N=3 might be close to N=infinity. I describe calculations of the low-lying `glueball' mass spectrum, of the string tensions of k-strings and of topological fluctuations for N=2,3,4,5. We find that mass ratios appear to show a rapid approach to the large-N limit, and, indeed, can be described all the way down to SU(2) using just a leading O(1/NxN) correction. We confirm that the smooth large-N limit we find is confining and is obtained by keeping a constant 't Hooft coupling. We find that the ratio of the k=2 string tension to the k=1 fundamental string tension is much less than the naive (unbound) value of 2 and is considerably greater than the naive bag model prediction; in fact we find that it is consistent, within quite small errors, with either the M(-theory)QCD-inspired conjecture or with `Casimir scaling'. Finally I describe calculations of the topological charge of the gauge fields. We observe that, as expected, the density of small-size instantons vanishes rapidly as N increases, while the topological susceptibility appears to have a non-zero N=infinity limit.
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