Computation of the string tension in four-dimensional Yang–Mills theory using large N reduction

Abstract

Continuum reduction and Monte Carlo simulation are used to calculate the heavy quark potential and the string tension in large N Yang-Mills theory in four dimensions. The potential is calculated out to a separation of nine lattice units on a lattice with extent six in each direction.

Rectangular Wilson loops at large N

“…Expressed in terms of our variables it is σξ 2 c | b I =0.182 = 2.2(3). The results of [20] are claimed to be compatible with [19] at infinite N . These results were obtained working at N = 37, 47, 59 on a 6 4 lattice at small values b = 0.345, 0.348, 0.350 assuming large-N reduction and including folded loops in the analysis.…”

“…The result of [20] seems to side with that of [19], but has too large errors to be sure. The systematic error is too big to claim evidence for a difference between the string tension extracted from Wilson loops and that extracted from Polyakov loop correlators by [19] in the continuum limit.…”

“…A previous estimate for the string tension at infinite N extracted from rectangular loops has been given in [20]. Expressed in terms of our variables it is σξ 2 c | b I =0.182 = 2.2(3).…”

Introductory lectures to large- QCD phenomenology and lattice results

“…As an example of results obtained in this approach, in ref. [88] the confining potential was computed up to distances equal to 9 lattice spacings from simulations on a lattice of linear size L = 6a.…”

Recent results in large-N lattice gauge theories

“…As an example of results obtained in this approach, in ref. [66] the confining potential was computed up to distances equal to 9 lattice spacings, from simulations on a lattice of linear size L = 6a.…”